development of an internal camera-based volume

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Graduate Theses and Dissertations

12-2017

Development of an Internal Camera-Based Volume Determination Development of an Internal Camera-Based Volume Determination

System for Triaxial Testing System for Triaxial Testing

Sean Elliott Salazar University of Arkansas, Fayetteville

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Development of an Internal Camera-Based Volume Determination System for Triaxial Testing

A thesis submitted in partial fulfillment

of the requirements for the degree of

Master of Science in Civil Engineering

by

Sean Elliott Salazar

University of Arkansas

Bachelor of Science in Civil Engineering, 2013

December 2017

University of Arkansas

This thesis is approved for recommendation to the Graduate Council.

Dr. Richard Coffman

Thesis Director

Dr. Michelle Bernhardt-Barry Dr. Thomas Oommen

Committee Member Committee Member

ABSTRACT

Accurate measurement of axial, radial, and volumetric strain parameters are critical to

the understanding of phase relationships and the constitutive behavior for saturated and

unsaturated soils. The use of photographic monitoring techniques for laboratory-based

measurement of these parameters have become common. A novel technique that utilized camera

instrumentation located within the triaxial testing cell was developed and validated. By placing

the instrumentation inside of the cell, instead of the instrumentation being located outside of the

cell, the technique eliminated cumbersome corrections required to account for optical distortions

due to 1) the refraction of light at the confining fluid-cell wall-atmosphere interfaces, 2) the

curvature of the cylindrical cell wall, and 3) the deformation of the cell wall induced by changes

in cell pressure. Digital images of various soil and analog (brass, acrylic) specimens were

captured within the triaxial apparatus during testing. The images were processed using the

principles of close-range photogrammetry to construct three-dimensional models of the

specimens. The models were analysed to determine surface deformation and total volume of the

specimens. Additionally, the models obtained from triaxial tests performed on the soil samples

were compared to quantify deformation and volume of the sample as a function of axial strain.

Sensitivity studies and evaluation of measurement accuracy for the internal, close-range

photogrammetry approach are documented herein. Specimen volume, as obtained using the

approach, was compared with volume obtained from four other techniques, including: DSLR

camera photogrammetry, 3D structured light scanning, manual measurements (caliper and pi

tape), and water displacement. A relative error of 0.13 percent was assessed for the internal

photogrammetry technique. The viability of determining total and local strains, volumetric

changes, and total volume at any stage of triaxial testing was demonstrated through undrained

triaxial compression and extension tests. Results from all tests are presented herein. The use of

the internal, close-range photogrammetry technique is recommended.

ACKNOWLEDGEMENTS

A portion of this material is based upon work supported by the National Science

Foundation Graduate Research Fellowship Program under Grant No. DGE-1450079, as awarded

to Sean Salazar. Any opinions, findings, and conclusions or recommendations expressed in this

material are those of the author and do not necessarily reflect the views of the National Science

Foundation. The author would also like to acknowledge 1) support from the University of

Arkansas Provost Collaborative Research Grant, awarded to Richard Coffman (PI), Michelle

Bernhardt (Co-PI) and Adam Barnes (Co-PI), and 2) undergraduate student support from the

United States Department of Transportation (USDOT) Office of the Assistant Secretary for

Research and Technology (OST-R) under Research and Innovation Technology Administration

(RITA) Cooperative Agreement Award No. OASRTRS-14-H-UARK, awarded to Richard

Coffman (PI) and Thomas Oommen (Co-PI).

DEDICATION

I would like to dedicate this thesis to my mother, Betty, to my father, John, to my

grandfather, (Grandpop) Joe, to my brother, Eric, to my sister, Rachel, and to my wife,

Alexandra. Without their love, strength, and unending support, I could not have completed this

work. I would also like to acknowledge the guidance, encouragement, and leadership, of my

advisor, Dr. Richard Coffman. Finally, I would like to thank those colleagues and friends that

helped me along the way, in no particular order, Adam Barnes, Johnathan Blanchard, Cyrus

Garner, Mark Kuss, Nabeel Mahmood, Leah Miramontes, Guilherme Pontes, Morgan Race,

Andrew Schriver, and Brendan Yarborough.

TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION .................................................................................................1

1.1. Chapter Overview .................................................................................................................1

1.2. Description of the Work ........................................................................................................1

1.3. Motivation .............................................................................................................................3

1.3.1. Limitations of Current Techniques .................................................................................3

1.3.2. Contribution to Geotechnical Engineering .....................................................................4

1.4. Document Overview .............................................................................................................5

1.5. References .............................................................................................................................7

CHAPTER 2: BACKROUND ......................................................................................................9

2.1. Chapter Overview .................................................................................................................9

2.2. Parameters of Interest for Triaxial Testing of Soils ..............................................................9

2.3. Non-Photograph-Based Soil Specimen Monitoring Methods .............................................11

2.4. Photograph-Based Soil Specimen Monitoring Methods .....................................................14

2.4.1. Digital Image Analysis Techniques ..............................................................................14

2.4.2. Photogrammetric Techniques .......................................................................................17

2.5. References ...........................................................................................................................24

CHAPTER 3: CONSIDERATION OF INTERNAL BOARD CAMERA OPTICS FOR

TRIAXIAL TESTING APPLICATIONS..................................................................................29

3.1. Chapter Overview ...............................................................................................................29

3.2. Limitations of the Described Study .....................................................................................29

3.3. Consideration of Internal Board Camera Optics for Triaxial Testing Applications ...........30

3.4. Abstract ...............................................................................................................................30

3.5. Introduction .........................................................................................................................31

3.1. Background .........................................................................................................................32

3.6.1. Lens Optics ...................................................................................................................32

3.6.2. Pinhole Aperture ...........................................................................................................33

3.6.3. Pressure Resistant Cameras ..........................................................................................35

3.7. Challenges Encountered ......................................................................................................36

3.7.1. Space Requirements .....................................................................................................37

3.7.2. Confining Fluid ............................................................................................................39

3.7.3. Focal Length .................................................................................................................40

3.7.4. Cell Pressure .................................................................................................................41

3.7.5. Specimen Coverage ......................................................................................................41

3.8. Pinhole Solution ..................................................................................................................43

3.8.1. Video Signal Acquisition .............................................................................................46

3.9. Images Collected .................................................................................................................46

3.10. Conclusions .......................................................................................................................50

3.10.1. Advantages and Limitations of a BCPA ....................................................................51

3.11. References .........................................................................................................................52

CHAPTER 4: DEVELOPMENT OF AN INTERNAL CAMERA-BASED VOLUME

DETERMINATION SYSTEM FOR TRIAXIAL TESTING ..................................................55



4.3. Development of an Internal Camera-Based Volume Determination System for Triaxial

Testing .................................................................................................................................56

4.4. Abstract ...............................................................................................................................56

4.5. Introduction .........................................................................................................................56

4.6. Background .........................................................................................................................57

4.7. Internal Camera-Monitoring System ...................................................................................60

4.7.1. Mechanical Design .......................................................................................................61

4.7.2. Electrical Design ..........................................................................................................62

4.8. Photogrammetric Methods and Results ...............................................................................64

4.9. Conclusions .........................................................................................................................69

4.10. References .........................................................................................................................70

CHAPTER 5: DISCUSSION OF "A PHOTOGRAMMETRY-BASED METHOD TO

MEASURE TOTAL AND LOCAL VOLUME CHANGES OF UNSATURATED SOILS

DURING TRIAXIAL TESTING" BY ZHANG ET AL., 2015 ...............................................73


5.2. Discussion of "A Photogrammetry-based Method to Measure Total and Local Volume

Changes of Unsaturated Soils During Triaxial Testing" by Zhang et al., 2015 ..................73

5.3. Discussion ...........................................................................................................................74

5.3.1. Improper Triaxial Testing Techniques .........................................................................75

5.3.2. Utilization of Cell Wall Deformation Combined with Least-Square Optimization .....76

5.3.3. Testing Procedures and Photogrammetric Methods .....................................................78

5.4. References ...........................................................................................................................82

CHAPTER 6: CLOSURE TO "DISCUSSION OF 'DEVELOPMENT OF AN INTERNAL

CAMERA-BASED VOLUME DETERMINATION SYSTEM FOR TRIAXIAL TESTING'

BY S. E. SALAZAR, A. BARNES, AND R. A. COFFMAN" BY MEHDIZADEH ET AL.,

2016................................................................................................................................................83


6.2. Closure to "Discussion of 'Development of an Internal Camera-Based Volume

Determination System for Triaxial Testing' by S. E. Salazar, A. Barnes, and R. A.

Coffman" by Mehdizadeh et al., 2016.................................................................................83

6.3. Abstract ...............................................................................................................................83

6.4. Introduction .........................................................................................................................84

6.5. References ...........................................................................................................................94

CHAPTER 7: VERIFICATION OF AN INTERNAL CLOSE-RANGE

PHOTOGRAMMETRY APPROACH FOR VOLUME DETERMINATION DURING

TRIAXIAL TESTING .................................................................................................................96



7.3. Verification of an Internal Close-Range Photogrammetry Approach for Volume

Determination During Triaxial Testing ...............................................................................97

7.4. Abstract ...............................................................................................................................97

7.5. Introduction and Background ..............................................................................................98

7.6. Evaluation of the Internal Photogrammetry Technique ....................................................101

7.6.1. Calibration of Board Cameras ....................................................................................104

7.6.2. Derivation of Camera Stations within the Triaxial Cell .............................................105

7.6.3. Determination of Photograph-Capturing Intervals .....................................................106

7.6.4. Capture of Photographs to Determine Accuracy in Confining Fluid .........................107

7.6.5. Photogrammetric Reconstruction of a Specimen .......................................................108

7.6.6. Determination of a Specimen Volume .......................................................................110

7.6.7. Accuracy of Technique ...............................................................................................110

7.6.7.1. DSLR Camera Photogrammetry .........................................................................111

7.6.7.2. 3D Scanning ........................................................................................................112

7.6.7.3. Manual Measurements ........................................................................................113

7.6.7.4. Water Displacement ............................................................................................114

7.6.8. Limitations and Sources of Error ...............................................................................114

7.6.8.1. Precision of Repeat Interval Stops ......................................................................115

7.6.8.2. Model Refinement ..............................................................................................116

7.6.8.3. External Geometry Measurements ......................................................................116

7.6.8.4. Determination of Specimen Ends .......................................................................116

7.7. Implementation of the Internal Photogrammetry Technique for Soil Specimens .............117

7.8. Results and Discussion ......................................................................................................121

7.8.1. Volume Comparisons .................................................................................................121

7.8.2. Photograph Interval ....................................................................................................123

7.8.3. Testing of Internal Photogrammetry System on Soil Specimens ...............................124

7.9. Conclusions .......................................................................................................................129

7.9.1. Potential Applications and Future Improvements ......................................................130

7.10. Acknowledgements .........................................................................................................131

7.11. References .......................................................................................................................132

CHAPTER 8: CONCLUSIONS ...............................................................................................135

8.1. Chapter Overview .............................................................................................................136

8.2. Highlights ..........................................................................................................................136

8.3. Limitations ........................................................................................................................137

8.4. Recommendations .............................................................................................................137

CHAPTER 9: WORKS CITED ................................................................................................139

LIST OF FIGURES

Figure 1.1. Exploded, transparent view of the major components of the internal camera-based

photogrammetry system (note: shown with piezoelectric end caps)…………………...…2

Figure 1.2. Overview of the evaluation process for the internal cell photogrammetry technique

presented in this document (modified from Salazar et al. 2017b)…………………….......3

Figure 2.1. Typical measurements and calculations required to determine the phase diagram of

the soil specimen during a reduced triaxial extension test (modified from Salazar et al.

2017b)…………………………………………………………………............................11

Figure 2.2. Schematic of a double-cell volume measuring system for triaxial testing of

unsaturated soils (from Ng et al. 2002)…………….………………………………….....12

Figure 2.3. Plan view schematic of laser scanning device for triaxial testing (from Messerklinger

and Springman 2007)………………………………………………………………….....14

Figure 2.4. Triaxial testing apparatus with (a) a single, fixed digital camera located outside of the

cell (from Gachet et al. 2007), and (b) three, fixed digital cameras located outside of the

cell (from Bhandari et al. 2012)……………………………………………………….....17

Figure 2.5. Optical magnification of soil specimen due to presence of confining fluid…………18

Figure 2.6. (a) Schematic of photogrammetric principles involved in the Zhang et al. (2015) and

Li et al. (2016) methodology, including (b) optical ray tracing, and (c) least-square

estimation (from Li et al. 2016)……………………………………………………….....20

Figure 2.7. Representation of specimen deformations obtained during a triaxial test (modified

from Li et al. 2016)………………………………………………………………………20

Figure 2.8. Schematic of board camera device with pinhole aperture developed at the University

of Arkansas (from Salazar and Coffman 2015)……………………………………….....22

Figure 2.9. Schematic of internal camera-based photogrammetry system for triaxial testing

developed at the University of Arkansas (modified from Salazar et al. 2015)…………..22

Figure 2.10. Representation of specimen deformation obtained from close-range

photogrammetry during an undrained, conventional, triaxial compression test (modified

from Salazar et al. 2017b)………………………………………………………………..23

Figure 3.1. Real image formation illustrated by simplified ray diagram of (a) diffraction of light

through a pinhole aperture, and (b) refraction of light through a lens…………………...35

Figure 3.2. The process that was followed to address the interrelated challenges in the design of

the BCPA………………………………………………………………………………...37

Figure 3.3. (a) Three types of board cameras that were tested, and (b) five different types of

lenses used with the cameras…………………………………………………………….39

Figure 3.4. Schematic of guided camera track system mounted on triaxial apparatus base……..42

Figure 3.5. Schematic of (a) front view, (b) exploded side view, and (c) exploded orthogonal

view of the BCPA………………………………………………………………………..45

Figure 3.6. Photograph of one of the BCPA utilized inside of the triaxial cell……………….....45

Figure 3.7. Still frames captured using a 8.38mm (0.33 in.) format CCD board camera with

(1) 3.7mm button lens (55º FOV, M12×0.5 thread) in (a) air, and within (b) PSF-5cSt

silicone oil, and with (2) 75 μm diameter pinhole aperture (attached to a M12×0.5 barrel

with 6.5mm diameter opening) in (c) air, and within (d) PSF-5cSt silicone oil…………47

Figure 4.1. (a) Exploded view, and (b) elevation view of the internal components of the

combined BCPA monitoring system………………………………………………….....61

Figure 4.2. Photograph of the power switchboard for the BCPA devices (power supply and

timing sequence)…………………………………………………………………………63

Figure 4.3. Wiring diagram of the photogrammetric instrumentation…………………………...64

Figure 4.4. (a) PhotoModeler camera calibration grid, (b) DSLR-acquired survey images

(control point identification), (c) BCPA-acquired calibration images (camera location

and orientation identification), and (d) BCPA-acquired images (point cloud

identification)………………………………………………………………………….....66

Figure 4.5. Vertically and horizontally overlapping photographs captured with two adjacent

BCPA on a single tower at 15º rotation intervals………………………………………..66

Figure 4.6. Photogrammetric reconstruction of BCPA locations within the triaxial cell for

(a) 45º, (b) 30º, (c) 15º, and (d) 5º rotation intervals………………………………...…..68

Figure 6.1. Comparison of deviatoric stress as a function of mean stress for a reduced triaxial

extension test with pauses and without pauses for capturing photographs………………91

Figure 6.2. Comparison of deviatoric stress as a function of axial strain for a reduced triaxial

extension test with pauses and without pauses for capturing photographs………………91

Figure 6.3. Comparison of excess pore water pressure development as a function of axial strain

for a reduced triaxial extension test with pauses and without pauses for capturing

photographs…………………………………………………………………………........92

Figure 7.1. The process used to evaluate the internal cell photogrammetry technique and to

obtain test parameters………………………………………………………………..…102

Figure 7.2. The process used to determine the volume of a specimen using internal cell

photogrammetry and to evaluate the sensitivity of photograph interval on the volume

of the specimen………...……………………………………………………………….103

Figure 7.3. (a) Photograph of, and (b) three-dimensional, watertight model of small-acrylic

analog specimen with spherical adhesive targets (removed during processing), as

obtained during 3D scanning of specimen………………………………………...........113

Figure 7.4. Qualitative factors affecting accuracy in photogrammetry (modified from Eos

Systems, Inc. 2015)……………………………………………………………………..115

Figure 7.5. Typical measurements and calculations required to determine the phase diagram of

the soil specimen during for conventional triaxial compression test………...................118

Figure 7.6. Photograph of the kaolinite specimen within the photogrammetrically instrumented

triaxial cell during the shearing stage of the extension test…………………………….120

Figure 7.7. Sensitivity of derived camera location difference to interval between

photographs……………………………………………………………………………..124

Figure 7.8. Visualization of photogrammetry-obtained, three-dimensional models of kaolinite

specimen during K0-consolidation phase of triaxial test (warm colors indicate positive

deformation and cool colors indicate negative deformation)…………………………..127

Figure 7.9. Visualization of photogrammetry-obtained, three-dimensional models of kaolinite

test specimen during (a) conventional triaxial compression, and (b) reduced triaxial

extension tests up to 15 percent axial strain during shearing (warm colors indicate

positive deformation and cool colors indicate negative deformation)……………….....128

LIST OF TABLES

Table 3.1. Photogrammetric properties of the BCPA……………………………………………49

Table 7.1. Comparison of intrinsic camera parameters from calibration for all ten board cameras

utilized for internal photogrammetry…………………………………………………...105

Table 7.2. Comparison of small-acrylic analog specimen volumes as obtained using five different

techniques………………………………………………………………………………122

Table 7.3. Comparison of large-acrylic analog specimen volumes as determined during internal

photograph interval sensitivity test……………………………………………………..123

Table 7.4. Volumes of kaolinite soil specimens as determined throughout the triaxial

compression test and corresponding summary statistics……………………………….126

Table 7.5. Volumes of kaolinite soil specimen as determined throughout the triaxial extension

test and corresponding summary statistics……………………………………………...126

Table 7.6. Volumes of kaolinite soil specimen as determined throughout the unconfined

compression test and corresponding summary statistics……………………………….126

LIST OF SYMBOLS AND ACRONYMS

Symbol Definition

3D Three-dimensional

Ac Corrected area

Af Area of failure plane

BCPA Board Camera with Pinhole Aperture

CCD Charge-Coupled Device

cm Centimeter

CMOS Complementary Metal Oxide Semiconductor

CTC Conventional Triaxial Compression

DIA Digital Image Analysis

DIC Digital Image Correlation

DSLR Digital Single Lens Reflex

d Diameter

d0 Initial diameter

f Focal length

h0 Initial height

K0 Coefficient of lateral earth pressure at-rest

K1, K2, K3 Dimensionless coefficients of radial distortion

kPa Kilopascal

LoHR Lines of Horizontal Resolution

m Mass

mm Millimeter

MVS Multi-View Stereo

n1 Refractive index of lens material

n2 Refractive index of surrounding medium

OCR Overconsolidation Ratio

p' Mean stress

P1, P2 Dimensionless coefficients of decentering distortion

PIV Particle Image Velocimetry

psi Pounds per square inch

q Deviatoric stress

r Radius of the pinhole opening (aperture)

r1 Radius of curvature of front surface of lens

r2 Radius of curvature of back surface of lens

RAD Ringed Automatically Detected

RTE Reduced Triaxial Extension

SfM Structure from Motion

UC Unconfined Compression

V Volume

V0 Initial volume

VT Total volume

w Water content

wc Water content

Δd Change in diameter

Δh Change in height

Δu Excess pore pressure

ΔV Change in volume

εa Axial strain

εr Radial strain

εv Volumetric strain

λ Design wavelength

μm Micrometer

σ1 Major principal stress

σ3 Confining stress

º Degree

% Percent

LIST OF PUBLISHED OR SUBMITTED PAPERS

Chapter 3: Consideration of Internal Board Camera Optics for Triaxial Testing Applications.

Published as: Salazar, S.E., Coffman, R.A. (2015). “Consideration of Internal Board

Camera Optics for Triaxial Testing Applications.” Geotechnical Testing Journal,

Vol. 38, No. 1, pp. 40-49. doi:10.1520/GTJ20140163.

Chapter 4: Development of an Internal Camera-Based Volume Determination System for

Triaxial Testing. Published as: Salazar, S.E., Barnes, A., Coffman, R.A. (2015).

“Development of an Internal Camera-Based Volume Determination System for Triaxial

Testing.” Geotechnical Testing Journal, Vol. 38, No. 4, pp. 549-555.

doi:10.1520/GTJ20140249.

Chapter 5: Discussion of “A Photogrammetry-based Method to Measure Total and Local

Volume Changes of Unsaturated Soils During Triaxial Testing” by Zhang et al., 2015.

Published as: Salazar, S.E., Coffman, R.A. (2015). “Discussion of ‘A Photogrammetry-

based Method to Measure Total and Local Volume Changes of Unsaturated Soils During

Triaxial Testing’ by Zhang et al.” Acta Geotechnica, Vol. 10, No. 5, pp. 693-696.

doi:10.1007/s11440-015-0380-1.

Chapter 6: Closure to “Discussion of ‘Development of an Internal Camera-Based Volume

Determination System for Triaxial Testing’ by S. E. Salazar, A. Barnes, and R. A.

Coffman” by Mehdizadeh et al., 2016. Published as: Salazar, S.E., Barnes, A., Coffman,

R.A. (2017). “Closure to “Discussion of ‘Development of an Internal Camera-Based

Volume Determination System for Triaxial Testing’ S.E. Salazar, A. Barnes, and R.A.

Coffman” by A. Mehdizadeh, M.M. Disfani, R. Evans, A. Arulrajah and D.E.L. Ong.”

Geotechnical Testing Journal. Vol. 40, No. 1, pp. 47-51. doi:10.1520/GTJ20160154.

Chapter 7: Verification of an Internal Close-Range Photogrammetry Approach for Volume

Determination During Triaxial Testing. Submitted as: Salazar, S.E., Miramontes, L.D.,

Barnes, A.R., Bernhardt, M.L., Coffman, R.A. (2017). “Verification of an Internal Close-

Range Photogrammetry Approach for Volume Determination During Triaxial Testing.”

Geotechnical Testing Journal. Submitted for Review. Manuscript Number: GTJ-2017-

0125.R2.

1

CHAPTER 1: INTRODUCTION

1.1. Chapter Overview

The development of an internal camera-based volume determination system for triaxial

testing is described in this document. The system was used in conjunction with a close-range

photogrammetry technique to 1) capture digital images, 2) photogrammetrically construct three-

dimensional models, and 3) calculate the volume and deformation for soil specimens during all

stages of triaxial compression and triaxial extension tests. This chapter is subdivided into four

sections. A brief overview of the work that is described in this document is contained in Section

1.2. The motivation for conducting this research is described in Section 1.3. An overview of the

entire document is presented in Section 1.4.

1.2. Description of the Work

The development of the internal camera-based instrumentation for triaxial cell

photogrammetry and the associated data collection and processing techniques are described in

this document. The development is also briefly described in this section. A set of ten small board

cameras was designed and incorporated into two, diametrically opposed, camera towers. Each

tower, with five camera devices, was mounted to a rotational track within the cell; the towers

were free to rotate about the soil specimen during triaxial testing. At any desired stage during the

triaxial test (e.g. at a given axial strain level during shearing), the test was paused and the camera

towers were rotated incrementally about the specimen while capturing images of the specimen.

To facilitate measurements during the triaxial test, the entire system was designed to be

incorporated into the triaxial cell to be in direct contact with the confining fluid. A rendering of

the camera instrumentation, as mounted inside of the triaxial cell, is presented as Figure 1.1.

2

Figure 1.1. Exploded, transparent view of the major components of the internal camera-

based photogrammetry system (note: shown with piezoelectric transducer end caps).

The images that were collected with the system were processed using a close-range

photogrammetry technique to 1) construct the digital surface of the specimen, and 2) determine

the total volume of the specimen. To demonstrate the viability of the technique for triaxial tests,

one conventional triaxial compression test and one reduced triaxial extension test was performed.

During each test, images of the specimen were captured for various levels of axial strain and a

three-dimensional model was created for each of the various axial strain levels. To evaluate the

accuracy of the internal photogrammetry technique, several validation tests were performed.

Specifically, the technique was evaluated using analog specimens (one brass and two acrylic

specimens). The effect of the number of images on the reconstruction of a specimen (ranging

from 40 to 320 images) was examined and the total volume of the specimens that were obtained

Triaxial testing cell base

Cell wall

Individual board camera device

Soil specimen with photogrammetric targets on membrane

Camera tower

Rotating track

Magnet

3

were compared with volumes measured using four other methods. An overview of the evaluation

steps is presented as Figure 1.2.

Figure 1.2. Overview of the evaluation process for the internal cell photogrammetry

technique presented in this document (modified from Salazar et al. 2017b).

1.3. Motivation

The motivation for the research conducted for this work is presented in this section. The

limitations of the techniques that are currently employed in the laboratory to monitor triaxial

specimens during testing are discussed in Section 1.3.1. The contribution of the work to the field

of geotechnical engineering is discussed in Section 1.3.2.

1.3.1. Limitations of Current Techniques

Various methods have been employed by researchers to monitor soil specimens during

triaxial tests. These monitoring efforts have enabled one or more of the following: 1)

measurement of axial and/or radial dimensions and deformations during testing, 2) measurement

Volu

mes C

alc

ula

ted

3-D Scan

DSLR Camera Photogrammetry

Manual Measurements

Water Displacement

Comparison of Volumes

CTC and RTE Testing of Soil Specimens

Capture photos of specimen with camera towers at 20° rotation interval

for any given stage of testing

DSLR Target Identification

Internal Camera Location/Orientation

Create 3-D volumes of specimen for any given stage of testing

Calculate specimen parameters Visualize strains

Internal Cell Photogrammetry Evaluation

Volume Determination

Method Comparison

Internal Cell Photogrammetry

4

of local and/or total volume, 3) calculation of axial, radial, and/or volumetric strains, and 4)

characterization of shear banding behavior. Techniques that have been described in the literature

include double-wall cell systems (e.g. Bishop and Donald 1961), differential pressure transducers

(e.g. Ng et al. 2002), measurements of air and water volume changes (e.g. Leong et al. 2004),

displacement and strain sensors (e.g. Scholey et al. 1995), non-contact proximity sensors (e.g.

Clayton et al. 1989), laser scanners (e.g. Messerklinger and Springman 2007), digital image

analysis (e.g. Bhandari et al. 2012), x-ray computed tomography (e.g. Viggiani et al. 2004), and

photogrammetry (e.g. Zhang et al. 2015). Broadly speaking, these techniques can be divided into

photograph-based and non-photograph-based categories.

In recent years, photograph-based methods have achieved prominence due to their

practicality, cost-effectiveness, and versatility. Furthermore, many of the non-photograph-based

techniques suffered from poor data resolution, relied heavily on geometric assumptions, and

often required installation of complex and expensive instrumentation. However, even the

photograph-based techniques have been limited by poor resolution, and the need to perform

computationally intensive corrections to overcome distortions caused by the confining fluid and

the cell wall surrounding the soil specimen. The limitations of the photograph-based and non-

photograph-based approaches were discussed in detail in Salazar and Coffman (2015a, 2015b)

and Salazar et al. (2015, 2017a, 2017b). Based on a review of the existing literature, there was a

need for a better photogrammetry technique that relied upon cameras internal to the cell.

1.3.2. Contribution to Geotechnical Engineering

Testing of the novel Salazar and Coffman (2016) device, in conjunction with the close-

range photogrammetry technique detailed in Salazar et al. (2017b), was shown to be a viable

alternative to other photograph-based techniques. Moreover, the technique allowed for direct

5

observation and coverage of the entire radial surface of a specimen. This coverage resulted in

highly detailed construction of the three-dimensional surface of the specimen. Moreover, the

measurements were independent of any assumptions of initial dimensions or deformation

behavior. The technique simplified the computations required by other photogrammetric

methods, such as the method presented by Zhang et al. (2015). The potential for obtaining more

information about a given soil specimen, such as axial, radial, and volumetric strains during a

triaxial test is demonstrated by the technique that is presented in this document. This information

can be used together with the other soil parameters to improve the development of constitutive

models of soil. With continued improvements to the device and to the processing workflow, the

potential for less time-consuming data collection and data reduction is envisioned.

1.4. Document Overview

This document is comprised of nine chapters. In this chapter (Chapter 1), an overview of

the work contained within the document and the contribution of the work to the field of

geotechnical engineering were provided. The background for the work is presented in the form

of a literature review in Chapter 2. Five subsequent archival journal publications, on the subject

of this work, are presented in Chapters 3 through 7, in the order in which the manuscripts were

conceived and published. The process of developing suitable cameras for the internal

photogrammetry system is described in Chapter 3. The development of the mechanical,

electrical, and photogrammetric components of the system is described in Chapter 4. A

discussion of the paper by Zhang et al. (2015), on the topic of photogrammetry for triaxial

testing, is included as Chapter 5. A closure to a discussion paper written by Mehdizadeh et al.

(2016) on the Salazar et al. (2015) publication is included as Chapter 6. The validation of the

internal, close-range photogrammetry approach for triaxial testing is described in Chapter 7.

6

Conclusions drawn from the work presented in Chapter 3 through Chapter 7 are discussed in

Chapter 8. Finally, a comprehensive list of works cited in this document is included as Chapter 9.

7

1.5. References

Bhandari, A. R., Powrie, W., and Harkness, R. M., 2012, “A Digital Image-Based Deformation

Measurement System for Triaxial Tests,” Geotech. Test. J., Vol. 35, No. 2, pp. 1-18.

Bishop, A. W. and Donald, I. B., 1961, “The Experimental Study of Partly Saturated Soil in

Triaxial Apparatus,” Proceedings of the Fifth International Conference on Soil

Mechanics and Foundation Engineering, Vols. 1/3, Paris, July 17–22, Institution of Civil

Engineers, London, pp. 13–21.

Clayton, C. R. I., Khatrush, S. A., Adriano, V. D. B., and Siddique, A., 1989, “The Use of Hall

Effect Semiconductors in Geotechnical Instrumentation,” Geotech. Test. J., Vol. 12,

No. 1, pp. 69-76.

Kikkawa, N., Nakata, Y., Hyodo, M., Murata, H., and Nishio, S., 2006, "Three-Dimensional

Measurement of Local Strain Using Digital Stereo Photogrammetry in the Triaxial Test,"

Geomechanics and Geotechnics of Particulate Media, M. Hyodo, H. Murata, and Y.

Nakata, Eds., Taylor and Francis, London, pp. 61-67.

Leong, E.C., Agus, S.S., and Rahardjo, H., 2004, “Volume Change Measurement of Soil

Specimen in Triaxial Test,” Geotech. Test. J., Vol. 27, No. 1, pp. 47-56.

Mehdizadeh, A., Disfani, M. M., Evans, R., Arulrajah, A., and Ong, D. E. L., 2016, “Discussion

of ‘Development of an Internal Camera-Based Volume Determination System for

Triaxial Testing’ by S. E. Salazar, A. Barnes and R. A. Coffman

(doi:10.1520/GTJ20140249).” Geotech. Test J., Vol. 39, No. 1, pp. 165-168.

doi:10.1520/GTJ20150153.

Messerklinger, S. and Springman, S. M., 2007, “Local Radial Displacement Measurements of

Soil Specimens in a Triaxial Test Apparatus Using Laser Transducers,” Geotech. Test. J.,

Vol. 30, No. 6, pp. 1-12.

Ng, C. W. W., Zhan L. T., and Cui Y. J., 2002, “A New Simple System for Measuring Volume

Changes in Unsaturated Soils,” Can. Geotech. J., Vol. 39, No. 3, pp. 757-764.

Salazar, S. E., Barnes, A., and Coffman, R. A., 2015, “Development of an Internal Camera

Based Volume Determination System for Triaxial Testing,” Geotech. Test. J., Vol. 38,

No. 4, pp. 549-555. doi:10.1520/GTJ20140249.

Salazar, S. E., Barnes, A., and Coffman, R. A., 2017a, “Closure to “Discussion of ‘Development

of an Internal Camera-Based Volume Determination System for Triaxial Testing’ S. E.

Salazar, A. Barnes and R. A. Coffman” by A. Mehdizadeh, M. M. Disfani, R. Evans, A.

Arulrajah and D. E. L. Ong,” Geotech. Test. J., Vol. 40, No. 1, pp. 47-51.

doi:10.1520/GTJ20160154.

8

Salazar, S. E. and Coffman, R. A., 2015a, “Consideration of Internal Board Camera Optics for

Triaxial Testing Applications,” Geotech. Test. J., Vol. 38, No. 1, pp. 40-49.

doi:10.1520/GTJ20140163.

Salazar, S. E. and Coffman, R. A., 2015b, “Discussion of “A Photogrammetry-Based Method to

Measure Total and Local Volume Changes of Unsaturated Soils During Triaxial Testing”

by Zhang et al. (doi:10.1007/s11440-014-0346-8)” Acta Geotech., Vol. 10, No. 5,

pp. 693-696. doi:10.1007/s11440-015-0380-1.

Salazar, S. E. and Coffman, R. A., 2016, “Pressurized Fluid-Submerged, Internal, Close-Range

Photogrammetry System for Laboratory Testing,” U.S. Patent and Trademark Office.

Patent 15/360,820. Filed November, 2016.

Salazar, S. E., Miramontes, L. D., Barnes, A., Bernhardt, M. L., and Coffman, R. A., 2017b,

“Verification of an Internal Close-Range Photogrammetry Approach for Volume

Determination During Triaxial Testing,” Geotech. Test. J. Submitted for Review.

Manuscript Number: GTJ-2017-0125.R2.

Scholey, G. K., Frost, J. D., Lo Presti, C. F., and Jamiolkowski, M., 1995, “A Review of

Instrumentation for Measuring Small Strains During Triaxial Testing of Soil Specimens,”

Geotech. Test. J., Vol. 18, No. 2, pp. 137–156.

Viggiani, G., Lenoir, N., Bésuelle, P., Di Michiel, M., Marello, S., Desrues, J., and Kretzschmer,

M., 2004, “X-ray Microtomography for Studying Localized Deformation in Fine-Grained

Geomaterials Under Triaxial Compression,” Cr Acad Sci II B-Mec, Vol. 332,

pp. 819-826.

Zhang, X., Li, L., Chen, G., and Lytton, R., 2015, “A Photogrammetry-Based Method to

Measure Total and Local Volume Changes of Unsaturated Soils During Triaxial

Testing,” Acta Geotechnica, Vol. 10, No. 1, pp. 55-82. doi:10.1007/s11440-014-0346-8.

9

CHAPTER 2: BACKGROUND


A review of the relevant literature is contained within this chapter. The parameters of

interest for triaxial testing of saturated and unsaturated soils are presented in Section 2.2. An

overview of non-photograph-based soil specimen monitoring methods, with a focus on triaxial

testing, is provided in Section 2.3. A summary of the literature related to photograph-based soil

specimen monitoring, with a focus on triaxial testing, is presented in Section 2.4. Subsections for

digital image analysis techniques (Section 2.4.1) and photogrammetric techniques (Section 2.4.2)

are contained within Section 2.4.

2.2. Parameters of Interest for Triaxial Testing of Soils

Numerous techniques have been applied to study the volume and strain evolutions for

saturated and unsaturated soil specimens during triaxial tests. The practice of measuring changes

in volume during a test has become routine for many laboratories and is critical for triaxial

testing of unsaturated soils. The parameters of interest for a given triaxial test typically include:

1) total and local volume changes, and 2) axial, radial, and volumetric strains. Although there are

several methods for indirectly obtaining or calculating these parameters, assumptions of elastic

and uniform deformation behaviors to estimate shape are typically associated with this approach.

An example of one set of calculations for obtaining axial, radial, and volumetric strains during an

undrained triaxial test is presented in Equations 2.1, 2.2, and 2.3, respectively. This method relies

on a geometric estimation of specimen shape after deformation and relies on relative changes in

specimen dimensions. Ehrgott (1971) presented five additional variations of the equations used

to calculate the strains, but all of the variations suffer from fundamentally flawed assumptions

regarding the specimen shape.

10

𝜀𝑎 =𝛥ℎ

ℎ0 (modified from Ehrgott 1971) Equation 2.1

𝜀𝑟 =𝛥𝑑

𝑑0 (modified from Ehrgott 1971) Equation 2.2

𝜀𝑣 =𝛥𝑉

𝑉0= 𝜀𝑎 + 𝜀𝑟 − 𝜀𝑟𝜀𝑎 +

𝜀𝑟2

3(𝜀𝑎 − 1) (modified from Ehrgott 1971) Equation 2.3

Where εa is axial strain, Δh and h0 are change in height and initial height of a test specimen,

respectively, εr is radial strain, Δd and d0 are change in diameter and initial diameter of a test

specimen, respectively, εv is volumetric strain, and ΔV and V0 are change in volume and initial

volume of a test specimen, respectively.

To further illustrate an example of the assumptions that are typically made regarding the

specimen deformation behavior during a triaxial test, the five testing stages of a reduced triaxial

extension test are illustrated in Figure 2.1. It is commonly assumed that the specimen deforms as

a perfect, right, circular cylinder (ASTM D4767, 2011). Therefore, this technique is not suitable

for obtaining the correct area of the failure plane and the resulting shear strength calculations for

the specimen are inaccurate. Due to these inaccuracies, researchers have turned to a variety of

techniques to directly measure the parameters of interest during triaxial testing.

11

1. Pre-test: Mass (m) and water content (w), measured; Volume (V) calculated using caliper measurements. 2. Back-pressure saturation: Drain lines filled. Total volume change (ΔV) from pore pump measurements. This volume change includes air 1) purged from lines, and 2) going into suspension. 3. K0 Consolidation: Sample ΔV from pore pump measurements. 4. Shearing: m, w, and V assumed to be equal to post-test m, w, and V (if undrained); calculated from pore pump measurements (if drained). 5. Post-test: m and w, measured. Shear strength determined based on corrected area (Ac).

Figure 2.1. Typical measurements and calculations required to determine the phase

diagram of the soil specimen during a reduced triaxial extension test (modified from

Salazar et al. 2017b).

2.3. Non-Photograph-Based Soil Specimen Monitoring Methods

Historically, changes in confining fluid or pore fluid volume have been directly

correlated with changes in specimen volume. However, volume measurements have been

influenced by temperature- and pressure-induced flexure of the cell wall and drain lines. Bishop

and Donald (1961) modified a standard triaxial testing apparatus to include a second, inner cell

that was filled with mercury to measure total changes in volume of a specimen. Other double-cell

techniques that relied on measuring the changes in volume of the confining fluid (water and/or

air) within the pressurized cell were introduced by Wheeler (1986), Cui and Delage (1996),

Toyota et al. (2001), Aversa and Nicotera (2002), and Ng et al. (2002). A review of these volume

measurement techniques was provided in Leong et al. (2004), which also contained a method for

correcting for the expansion of the confining fluid due to temperature fluctuations. An example

of a double-cell triaxial apparatus is presented as Figure 2.2.

1 2 3 4 5

12

To complement volume measurements, axial deformation measurements have also been

collected during testing. Changes in axial deformation have been used to calculate average

specimen dimensions by adding or subtracting deformation measurements from initial

dimensions, with the initial dimensions having been established prior to testing (typically by

means of caliper and pi tape measurements). Therefore, known or assumed specimen dimensions

were used to calculate axial, radial, or volumetric strains, as described in Section 2.2. However,

conventional axial (Scholey et al. 1995, Cuccovillo and Coop 1997, Ng and Chiu 2001) and

lateral or radial (Khan and Hoag 1979, Bésuelle and Desrues 2001) displacement transducer

measurements have relied on averaging methods and total volumetric changes that did not

accurately account for irregular deformation behavior, such as shear banding, bulging

bifurcation, or necking.

Figure 2.2. Schematic of a double-cell volume measuring system for triaxial testing of

unsaturated soils (from Ng et al. 2002).

13

Other measurement techniques have been employed to measure soil specimen

parameters. Clayton and Khatrush (1986) and Clayton et al. (1989) introduced a non-contact

proximity sensor technique to measure local radial and axial strains during triaxial testing.

Romero et al. (1997), Messerklinger and Springman (2007), and Jain et al. (2015) employed

laser-scanning devices. The aforementioned Romero et al. (1997) device was incorporated into a

suction- and temperature-controlled triaxial apparatus for the testing of unsaturated soils. Two

externally mounted, diametrically opposed lasers were utilized to measure the radial deformation

profile along the length of the specimen at two locations. Similarly, the Messerklinger and

Springman (2007) device was utilized to measure radial displacements for three vertical profiles

around the circumference of the specimen during triaxial testing (Figure 2.3). In both techniques,

the radial displacements between the measured profiles were inferred. Although the Jain et al.

(2015) device was not employed during triaxial tests, the technique utilized a fixed laser pointed

at a soil specimen placed on a rotating turntable. This allowed for continuous measurements of

the entire specimen surface at desired intervals during a shrinkage test and subsequent

calculation of specimen volume. Desrues et al. (1996) and Viggiani et al. (2004) utilized x-ray

computed tomography to study the triaxial soil specimens.

14

Figure 2.3. Plan view schematic of laser scanning device for triaxial testing (from

Messerklinger and Springman 2007).

2.4. Photograph-Based Soil Specimen Monitoring Methods

To overcome the limitations of the previously discussed techniques in Section 2.3, digital

imaging techniques have increasingly been employed to monitor soil specimens. Specifically,

these techniques have been used to 1) calculate the total volume and volumetric strain of soil

specimens and/or to 2) monitor the evolution of shear bands and local strains. The photograph-

based techniques have been shown to be robust alternatives to conventional measurement

techniques for obtaining measurements during triaxial testing. The photograph-based techniques

in the literature fall under one or more of the following classifications: Digital Image Analysis

(DIA), Digital Image Correlation (DIC), Particle Image Velocimetry (PIV), or photogrammetry.

For the purposes of this discussion, DIA, DIC, and PIV techniques have all been grouped under

the digital image analysis category, while photogrammetry technique is treated separately.

2.4.1. Digital Image Analysis Techniques

Throughout the literature, the terms DIA and DIC have sometimes been used

interchangeably and the distinctions of the methods are beyond the scope of this discussion.

15

Therefore, these methods are discussed together and are referred to collectively as DIA

techniques herein. DIA techniques have allowed for more information to be captured and

quantified for soils specimens. For example, Alshibli and Sture (1999) utilized a uniform grid

applied to the membrane of a triaxial soil specimen to measure displacements at the surface of

the specimen during the development of a shear band. In another set of examples, Gudehus and

Nübel (2004) and Rechenmacher and Finno (2004) both studied the evolution of shear bands in

sands during biaxial tests using digital image analysis. In yet another pair of examples, Ören et

al. (2006) and Önal et al. (2008) used digital image correlation to determine the volume of soil

specimens during shrinkage tests.

Another class of digital image analysis is PIV; PIV was developed by Adrian (1991) for

experimental fluid dynamics applications. Although PIV techniques share some common traits

with DIA techniques, PIV differs significantly from DIA. PIV techniques primarily utilize image

texture instead of target markers to track movement in sequential images. PIV has been used to

measure planar surface deformation and to analyze displacement and strain fields for various soil

tests. Examples of PIV techniques that have been employed to monitor soil specimens include

Guler et al. (1999), White et al. (2003), Iskander and Liu (2010), Stanier et al. (2016), and Pinyol

and Alvarado (2017). Because PIV techniques have not been shown to aid in the determination

of triaxial specimen volumes, these techniques are not further discussed.

The use of digital images in conjunction with DIA techniques for monitoring triaxial tests

has been presented in the literature. Examples include Macari et al. (1997), Alshibli and Sture

(1999), Alshibli and Al-Hamdan (2001), Gachet et al. (2007), Sachan and Penumadu (2007),

Rechenmacher and Medina-Cetina (2007), Uchaipichat et al. (2011), Bhandari et al. (2012), and

Hormdee et al. (2014). In each of these examples, digital images of the soil specimens were

16

captured during testing with photographic equipment that was located outside of the triaxial

testing cell. Although the entire length of the specimen (in the axial dimension) was captured

within a single image in each of the aforementioned references, various methods were used to

capture the entire surface area of the specimen in the lateral dimension. For example, Alshibli

and Al-Hamdan (2001) and Bhandari et al. (2012) placed multiple cameras at intervals around

the outside of the cell, whereas Macari et al. (1997) and Gachet et al. (2007) utilized only a

single, fixed camera and therefore did not capture the entire specimen surface. In other instances,

the entire specimen surface was not captured because only the zone of shear banding was of

interest (Liang et al. 1997, Alshibli and Sture 1999, Sachan and Penumadu 2007). In all cases,

proper lighting conditions were critical for collecting usable photographs for obtaining high

quality results with DIA techniques, as demonstrated by Gachet et al. (2007), Bhandari et al.

(2012), and Hormdee et al. (2014). Examples of the camera-based measurement apparatus are

presented in Figure 2.4.

17

(a) (b)

Figure 2.4. Triaxial testing apparatus with (a) a single, fixed digital camera located outside

of the cell (from Gachet et al. 2007), and (b) three, fixed digital cameras located outside of

the cell (from Bhandari et al. 2012).

2.4.2. Photogrammetric Techniques

All of the previously discussed methods for monitoring soil specimens during triaxial

tests utilized external cameras and therefore several optical challenges were encountered, as 1)

described in detail by Bhandari et al. (2012) and Salazar and Coffman (2015) and 2) as

illustrated in Figure 2.5. Although Kikkawa et al. (2006) first introduced a stereo

photogrammetry technique for measuring local displacement and volume for specimens in

triaxial compression, photogrammetric techniques for monitoring triaxial soil specimens did not

18

reappear in the literature until Salazar et al. (2015) and Zhang et al. (2015). The initial work by

Zhang et al. (2015) was extended by the same authors in Li et al. (2016) and the Salazar et al.

(2015) work was extended in Miramontes (2016) and Salazar et al. (2017a, 2017b). As stated by

Zhang et al. (2015), photogrammetric techniques were needed because of the significant

limitations and assumptions of other photographic methods (e.g. only local volume was

obtainable, or precise control of camera location and orientation were required for accurate

measurements).

Figure 2.5. Optical magnification of soil specimen due to presence of confining fluid.

19

The Zhang et al. (2015) and Li et al. (2016) technique involved acquiring photographs of

the specimen at various angles from outside of the cell wall using a single digital single lens

reflex (DSLR) camera. The images were then used to photogrammetrically construct a three-

dimensional model of the specimen, which was scaled to a real-world coordinate system to

obtain the local and total volume of the specimen for a given stage of testing. The Zhang et al.

(2015) and Li et al. (2016) method presented advantages of a photogrammetric approach by

overcoming many of the limitations of other photograph-based methods. However, the

implementation of the method introduced additional processing complexity by requiring

computationally intensive corrections to account for optical distortions. Specifically, a ray

tracing and least-squares optimization technique were utilized to correct for the light refraction at

the confining water–cell wall and cell wall–atmosphere interfaces, for the cell wall curvature,

and for the deformation of the cell wall under high confining pressures. A schematic illustrating

the photogrammetric principles involved with the Zhang et al. (2015) and Li et al. (2016)

technique is presented as Figure 2.6. The results obtained from the Zhang et al. (2015) and Li et

al. (2016) technique are presented as Figure 2.7.

20

Figure 2.6. (a) Schematic of photogrammetric principles involved in the Zhang et al. (2015)

and Li et al. (2016) methodology, including (b) optical ray tracing, and (c) least-square

estimation (from Li et al. 2016).

Figure 2.7. Representation of specimen deformations obtained during a triaxial test

(modified from Li et al. 2016).

21

Salazar and Coffman (2015, 2016) introduced novel camera instrumentation for

monitoring triaxial specimens during testing. A simple board camera device, modified with a

pinhole aperture (BCPA), was designed and incorporated into a camera system that was placed

inside of the triaxial testing cell. The camera device was designed to allow for immersion within

the confining fluid of the triaxial cell (silicone oil). The full immersion of the device caused the

air space behind the camera aperture to fill with the electronics-grade confining fluid, thereby

overcoming the need for a pressure-resistant housing. In addition to a pressure-resistant housing

being impractical for the high confining pressures reached during a triaxial test (up to 1,035

kPa), a pressure-resistant housing would have required more space than was available within the

triaxial cell. Furthermore, the immersion of the camera parts, including the charge-coupled

device (CCD) sensor within the fluid, allowed for direct observation of the soil specimen within

the triaxial cell. Using this technique, light only traveled through one medium (the confining

fluid). In tandem with the pinhole aperture, the need to account for image distortions introduced

by the differences in the indices of refraction of the various materials (lens, air, oil) was

eliminated. Schematics of the BCPA device and the internal camera system are presented as

Figure 2.8 and Figure 2.9, respectively.

22

Figure 2.8. Schematic of board camera device with pinhole aperture developed at the

University of Arkansas (from Salazar and Coffman 2015).

Figure 2.9. Schematic of internal camera-based photogrammetry system for triaxial testing

developed at the University of Arkansas (modified from Salazar et al. 2015).

23

As reported in Salazar et al. (2015, 2017a, 2017b), the internal camera system was used

to capture photographs of the entire specimen surface during a triaxial test by rotating the camera

towers around the specimen. Just as the Zhang et al. (2015) and Li et al. (2016) photogrammetry

technique relied on ringed automatically detected (RAD) targets, the Salazar et al. (2015, 2017)

technique also relied on RAD targets. In Salazar et al. (2015, 2017a, 2017b), the targets were

printed onto the membrane surrounding the specimen and were used to locate points on the

specimen surface. A close-range photogrammetry technique was then utilized to construct a

three-dimensional model of the specimen. Models that were obtained from various stages of

testing were scaled to a real-world coordinate system and then compared to obtain volumetric

changes. The models also allowed for virtual measurement of specimen dimensions. An example

of the results obtained from the Salazar et al. (2015, 2017a, 2017b) technique is presented as

Figure 2.10.

Figure 2.10. Representation of specimen deformation obtained from close-range

photogrammetry during an undrained, conventional, triaxial compression test (modified

from Salazar et al. 2017b).

24

2.5. References

Adrian, R. J., 1991, "Particle Imaging Techniques for Experimental Fluid Mechanics," Ann. Rev.

Fluid Mech., Vol. 23, No. 1, pp. 261-304.

Alshibli, K. A. and Sture, S., 1999, “Sand Shear Band Thickness Measurements by Digital

Imaging Techniques,” J. Comput. Civ. Eng., Vol. 13, No. 2, pp. 103–109.

Alshibli, K. A. and Al-Hamdan, M., 2001, “Estimating Volume Change of Triaxial Soil

Specimens From Planar Images,” Comput-Aid. Infrastruct. Eng., Vol. 16, No. 6,

pp. 415–421.

ASTM D4767-11, 2011, "Standard Test Methods for Consolidated Undrained

Triaxial Compression Test for Cohesive Soils," ASTM International, West

Conshohocken, PA, www.astm.org. doi:10.1520/D4767-11.

Aversa, S. and Nicotera, M. V., 2002, "A Triaxial and Oedometer Apparatus for Testing

Unsaturated Soils," Geotech. Test. J., Vol. 25, No. 1, pp. 3-15.

Bésuelle, P. and Desrues, J., 2001, “An Internal Instrumentation for Axial and Radial Strain

Measurements in Triaxial Tests,” Geotech. Test J., Vol. 24, No. 2, pp. 193-199.

Clayton, C. R. I. and Khatrush, S. A., 1986, "A New Device for Measuring Local Axial Strains

on Triaxial Specimens," Géotechnique, Vol. 36, No. 4, pp. 593-597.

Clayton, C. R. I., Khatrush, S. A., Bica, A. V. D., and Siddique, A., 1989, “The Use of Hall


No. 1, pp. 69–76.

Cuccovillo, T. and Coop, M. R., 1997, “The Measurement of Local Axial Strains in Triaxial

Tests Using LVDTs,” Géotechnique, Vol. 47, No. 1, pp. 167–171.

Cui, Y.J. and Delage, P., 1996, "Yielding and Plastic Behavior of an Unsaturated Compacted

Silt," Géotechnique, Vol. 46, No. 2, pp. 291-311.

Desrues, J., Chambon, R., Mokni, M., and Mazerolle, F., 1996, “Void Ratio Evolution Inside

Shear Bands in Triaxial Sand Specimens Studied by Computed Tomography.

Géotechnique, Vol. 46, No. 35, pp. 529-546.

Ehrgott, J. Q., 1971, "Calculation of Stress and Strain from Triaxial Test Data no Undrained Soil

Specimens," Miscellaneous Paper S-71-9, U.S. Army Engineer Waterways Experiment

Station, Vicksburg, Mississippi.

Gachet, P., Geiser, F., Laloui, L., and Vulliet, L., 2007, “Automated Digital Image Processing

for Volume Change Measurement in Triaxial Cells,” Geotech. Test. J., Vol. 30, No. 2,

pp. 98–103.

25

Gudehus, G. and Nübel, K., 2004, “Evolution of Shear Bands in Sand,” Géotechnique, Vol. 54,

No. 3, pp. 187–201.

Guler, M., Edil, T. B., and Bosscher, P. J., 1999, Measurement of Particle Movement in Granular

Soils Using Image Analysis," J. Comput. Civ., Vol. 13, No. 2, pp. 116-122.

Hormdee, D., Kaikeerati, N., and Jirawattana, P., 2014, “Application of Image Processing for

Volume Measurement in Multistage Triaxial Tests,” Adv. Mat. Res., Vol. 931-932,

pp. 501-505.

Iskander, M. and Liu, J., 2010, "Spatial Deformation Measurement Using Transparent Soil,"

Geotech. Test. J., Vol. 33, No. 4, 8 pgs.

Jain, S., Wang, Y. H., and Fredlund, D. G., 2015, "Non-Contact Sensing System to Measure

Specimen Volume During Shrinkage Test," Geotech. Test. J., Vol. 38, No. 6,

pp. 936-949. doi:10.1520/GTJ20140274.





Khan, M. H. and Hoag, D. L., 1979, “A Noncontacting Transducer for Measurement of Lateral

Strains,” Can. Geotech. J., Vol. 16, No. 2, pp. 409–411.

Leong, E. C., Agus, S. S., and Rahardjo, H., 2004, “Volume Change Measurement of Soil

Specimen in Triaxial Test,” Geotech. Test. J., Vol. 27, No. 1, pp. 47–56.

Li, L., Zhang, X., Chen, G., and Lytton, R., 2016, “Measuring Unsaturated Soil Deformations

During Triaxial Testing Using a Photogrammetry-Based Method,” Can. Geotech. J.,

Vol. 53, No. 3, pp. 472-489.

Liang, L., Saada, A., Figueroa, J. L., and Cope, C. T., 1997, “The Use of Digital Image

Processing in Monitoring Shear Band Development,” Geotech. Test. J., Vol. 20, No. 3,

pp. 324–339.

Macari, E. J., Parker, J. K., and Costes, N. C., 1997, “Measurement of Volume Changes in

Triaxial Tests Using Digital Imaging Techniques,” Geotech. Test. J., Vol. 20, No. 1,

pp. 103–109.





doi:10.1520/GTJ20150153.

26



Vol. 30, No. 6, pp. 1-12.

Miramontes, L. D., 2016, "Validation of an Internal Camera Based Volume Determination

System for Triaxial Testing," Civil Engineering Undergraduate Honors Theses. 33.

Ng, C. W. W. and Chiu, C. F., 2001, “Behaviour of a Loosely Compacted Unsaturated Volcanic

Soil,” J. Geotech. Geoenviron. Eng., Vol. 127, No. 12, pp. 1027–1036.



Önal, O., Ören, A. H., Özden, G., and Kaya, A., 2008, “Determination of Cylindrical Soil

Specimen Dimensions by Imaging With Applications to Volume Change of Bentonite–

Sand Mixtures,” Geotech. Test. J., Vol. 31, No. 2, pp. 124–131.

Ören, A. H., Önal, O., Özden, G., and Kaya, A., 2006, “Nondestructive Evaluation of

Volumetric Shrinkage of Compacted Mixtures Using Digital Image Analysis,”

Eng. Geol., Vol. 85, No. 3, pp. 239–250.

Pinyol, N. M. and Alvarado, M., 2017, "Novel Analysis for Large Strains Based on Particle

Image Velocimetry," Can. Geotech. J., Vol. 54, No. 7, pp. 933-944. doi:10.1139/cgj-

2016-0327.

Rechenmacher, A. L. and Finno, R. J., 2004, “Digital Image Correlation to Evaluate Shear

Banding in Dilative Sands,” Geotech. Test. J., Vol. 27, No. 1, pp. 13–22.

Rechenmacher, A. L. and Medina-Cetina, Z., 2007, “Calibration of Soil Constitutive Models

with Spatially Varying Parameters,” J. Geotech. Geoenviron., Vol. 133, No. 12,

pp. 1567–1576.

Romero, E., Facio, J. A., Lloret, A., Gens, A., and Alonso, E. E., 1997, “A New Suction and

Temperature Controlled Triaxial Apparatus,” presented at the Fourteenth International

Conference on Soil Mechanics and Foundation Engineering, Hamburg, Germany,

September 6-12, 1997, August Aimé Balkema, Amsterdam, pp. 185-188

Sachan, A. and Penumadu, D., 2007, “Strain Localization in Solid Cylindrical Clay Specimens

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pp. 619-631.

28




29

CHAPTER 3: CONSIDERATION OF INTERNAL BOARD CAMERA

OPTICS FOR TRIAXIAL TESTING APPLICATIONS


The concept of optics, internal to a triaxial testing cell, is explored in this chapter. The

challenges, limitations, and advantages associated with this concept are described and a simple

board camera modified with a pinhole aperture (BCPA) is introduced. The challenges of

implementing this camera system included limited space within the testing cell, the presence of

pressurized confining fluid within the cell, and sufficient photographic coverage of the entire

surface of a soil specimen. Preliminary testing of the camera device is presented and a system

that incorporated multiple devices attached to rotating fixtures within the cell are introduced.

The limitations of the included manuscript (Salazar and Coffman 2015) are discussed in

Section 3.2. The full citation for this document is included in Section 3.3. The motivation and

background for the manuscript are described in Sections 3.4, 3.5, and 3.6. Contained within

Section 3.7 are the challenges that were involved with designing a camera system capable of

acquiring images of a specimen from within the testing cell during a triaxial test. Section 3.8

contains a description of the BCPA device that overcame the presented challenges and Section

3.9 includes the testing and calibration of the BCPA device. Conclusions for this work are

presented in Section 3.10.

3.2. Limitations of the Described Study

The BCPA device that was designed for implementation within the internal camera-based

monitoring system suffered from relatively poor image quality, due to the nature of the pinhole

aperture and the low-cost board camera sensor. Although the BCPA overcame the presented

challenges, the optimization of the device required compromises in the field of view, resolution,

and light entry characteristics of the device. Although the study presented the concept of the

30

entire internal camera-based system, the results that were presented were focused primarily on

the development of the BCPA device and not on the system. Therefore, the manuscript presented

the development of the optics that had the potential for determination of specimen volumes.

3.3. Consideration of Internal Board Camera Optics for Triaxial Testing Applications

Reference

Salazar, Sean E. and Coffman, Richard A., “Consideration of Internal Board Camera Optics for

Triaxial Testing Applications,” Geotechnical Testing Journal, Vol. 38, No. 1, 2015, pp. 40-49.

doi:10.1520/GTJ20140163.

3.4. Abstract

The application of small board cameras, located within a triaxial cell to determine radial

and axial strain, was investigated. Specifically, charge-coupled device (CCD) sensors were

utilized in conjunction with precision pinhole apertures to capture images from within the triaxial

cell. The cameras were fully immersed in electronics-grade silicone oil and were able to

withstand cell pressures that are common to triaxial testing (up to 1034 kPa (150 psi)). The small

size of the cameras allowed for implementation within the triaxial cell, thereby avoiding: (1) the

cumbersome corrections that are required to account for refraction at the confining fluid–cell

wall–air interfaces and magnification due to cell wall curvature, and (2) the amount of space

required for outside-of-the-cell monitoring systems that utilize cameras. The final design of

the cameras was based on an iterative testing process in which various types of small board

cameras, lenses, and finally pinhole apertures were investigated. The advantages of the lensless

pinhole aperture camera design included: (1) lack of optical aberrations, such as those

encountered in traditional lensed camera systems, (2) practically infinite depth of field, allowing

for sharp, close-up images, and (3) wide-angle field of view without the distortions that are

associated with the use of wide-angle lenses. As discussed herein, the pinhole cameras were

optimized for optical resolution and light entry to minimize the effect of diffraction patterns that

31

are commonly associated with pinhole apertures. The resolution of the cameras was determined

to be sufficient for the potential application of the cameras (volume measurements). The

instrumentation presented herein provides a novel alternative to the state-of-the-art outside-of-

the-cell photogrammetric instrumentation that is currently employed to monitor soil specimens

during triaxial tests.

Keywords: photogrammetry, refraction, triaxial testing, laboratory equipment

3.5. Introduction

The current state-of-the-art photogrammetric technique for measuring the change in

volume of soil specimens located within a triaxial cell utilizes expensive digital cameras that are

located outside of the triaxial cell. The use of small board cameras located within the triaxial cell,

that overcome pressure and space constraints, has the potential to improve the current state-of-

the-art of photogrammetric techniques for triaxial testing, at a fraction of the expense. The

optical design of the board camera was of particular importance, as it was necessary to develop

high quality images within a confined space, while the camera was immersed in the confining

fluid. Therefore, a small open body board camera with a pinhole aperture (BCPA) was designed.

Although the use of board cameras with traditional lenses was attempted, the utilization of the

BCPA was proven to perform better than the lensed camera and the optical design was simpler,

more feasible, and more cost effective. The disadvantages of using a BCPA include (1) the

need for very precise aperture construction for acquisition of high quality imagery and (2)

limited resolution (when compared to traditional, lensed, outside-of-the-cell cameras). However,

the practical and economic advantages of using a BCPA far outweigh the disadvantages. The

basic optical principles of pinhole apertures and the existing state-of-the-art practice of obtaining

volume measurements using photogrammetry are described and the challenges encountered

32

during the design and fabrication of the BCPA are presented. The images obtained using the

BCPA, located within the triaxial cell, are compared with images obtained from traditional

lensed cameras, located within the triaxial cell, and the differences are discussed. Final remarks

and a summary of the BCPA system are also provided.

3.6. Background

Historically, when photogrammetric techniques were employed to measure the amount of

volume change in specimens being tested in a triaxial device, outside-of-the-cell cameras were

utilized (Parker 1987, Macari et al. 1997, Alshibli and Sture 1999, Alshibli and Al-Hamdan

2001, Gachet et al. 2006, Sachan and Penumadu 2007, Bhandari et al. 2012). However, light

refraction at the (1) confining fluid-cell wall interface and (2) cell wall-atmosphere interface and

the curvature of the cell wall have necessitated the use of models to account for the refraction

and magnification effects. Furthermore, the cameras surrounding the testing apparatus have been

expensive, limited by technology, and have required an excessive amount of space to develop the

required focal length and lighting conditions. Moreover, the optical elements of the camera

equipment have not been addressed in detail, such as optical aberrations, inherent to the camera

lenses.

3.6.1. Lens Optics

Lenses are typically used to capture and focus light and may be used to increase the field

of view. However, errors introduced by refraction of light through lenses, including spherical

aberration, coma, field curvature, astigmatism, and barrel, pincushion, and complex distortions

are prevalent to varying extents in lens applications (Mahajan 1998, Roichman et al. 2006,

Kingslake and Johnson 2010). Most camera lenses are therefore constructed of multiple lenses

(lens array) that are stacked to correct for some aberrations. A careful balance between

33

mitigating one type of aberration and augmenting another type has always existed; therefore, it is

never truly possible to capture an image that does not contain some type of aberration when a

lens or lens array is utilized. Although most cameras use lens arrays, liquid lenses (with variable

focus induced by an electrowetting process) have recently been developed for small applications

(Kuiper and Hendriks 2004, Hendriks et al. 2006, Nguyen 2010) to overcome aberrations

encountered with lenses and to adjust the focal length without the need for mechanical servo

action; liquid lenses are commonly utilized in many smart phone cameras. The aforementioned

focus (inverse of power) of a given lens may be calculated utilizing the Lensmaker’s equation

(Equation 3.1) for thin lenses, first developed by English physicist Thomas Young (1773–1829)

and later by Kuo and Ye (2004):

1

𝑓= (

𝑛1

𝑛2− 1) (

1

𝑟1−

1

𝑟2) Kuo and Ye (2004) Equation 3.1

Where f is the focal length of the lens, n1 is the refractive index of the lens material, n2 is the

refractive index of the surrounding medium, r1 is the radius of curvature of the front surface of

the lens, and r2 is the radius of curvature of the back surface of the lens.

3.6.2. Pinhole Aperture

The pinhole aperture camera is the most basic type of camera and is often overlooked in

favor of a lensed camera. However, despite, and perhaps because of its simplicity, the pinhole

camera may provide: (1) images free of the optical distortions that are inherent to the use of

lenses, (2) images with virtually infinite depth of field, (3) wide viewing angles, and (4) a

foundation for understanding the basic concepts involved in the field of optics, specifically

related to the use of cameras. The primary advantage of using a lens, as opposed to a simple

pinhole, is that a lens can capture and focus more light without requiring long exposure times,

thereby increasing optical resolution (defined as the ability to resolve detail). When resolution is

34

not the most critical objective of a camera application, a simple pinhole aperture camera may

provide a viable alternative to typical lensed camera. Pinholes have been used for centuries for

purposes of viewing and tracing images onto drawings prior to utilizing photo-sensitive materials

for photography purposes (Renner 2000). Moreover, the basic concepts of pinhole optics were

instrumental to the formulation of the theory of light. The theory was supported by the earliest

written observations of multiple phenomena related to light, specifically diffraction, interference,

and polarization of light through pinholes (Grimaldi 1665, Newton 1730, Young 1802, Fresnel

1819). According to Renner (2000), pinholes are still commonly utilized due to the

impracticality of using lenses. For example, scientific application of pinhole imaging may be

found in astro and nuclear physics (such as for high-energy particle imaging of laser plasma, X-

rays, the sun, black holes, and exploding stars).

The design of a pinhole aperture is relatively simple; however, certain considerations are

necessary to optimize image quality. Unlike lensed cameras, pinhole cameras rely on diffraction,

not refraction (Figure 3.1). The theory and equations for pinhole apertures were suggested by

early researchers like Herschel (1835), Airy (1835), and Strutt (1891); attempts have also been

made to refine the relationship between the optical phenomena in more recent years. However, as

Young (1971) indicates, the theoretical limits should only be used as a guideline because the

optimal pinhole aperture diameter is often better determined experimentally. The optimal pinhole

diameter is limited by resolution (larger diameters correspond with poorer resolution), by Fresnel

(near-field) and Fraunhofer (far-field) diffraction limits, and by the ability to gather light (smaller

diameters correspond with higher diffraction interference and allow less light to be collected).

The optimal pinhole diameter for optical applications often relates to the “Airy disk,” which is

the bright, focused spot, central to a diffraction pattern through a perfectly circular aperture.

35

Figure 3.1. Real image formation illustrated by simplified ray diagram of (a) diffraction of

light through a pinhole aperture, and (b) refraction of light through a lens.

3.6.3. Pressure Resistant Cameras

To be able to withstand high pressures, a camera is typically sealed in pressure-resistant

or, more commonly, pressure-compensating housings (Laudo et al. 1998). These housings are

typically bulky, expensive, and do not allow for direct optical observation because light must

first pass through a transparent thermoplastic barrier (i.e., acrylic plastic) before reaching the

camera. To combat this, fluids such as silicone oil or mineral oil (Salazar and Coffman 2014),

may be used in electronics applications where exposure to the fluid is unavoidable or desired.

The direct contact between the electronics and fluid will not cause short-circuiting due to the

inert and non-ionic properties of the oil (Mohapatra and Loikits 2005, Schmidt 2005, Lasance

and Simons 2005). Furthermore, even at high pressures, the silicone oil does not crush the

components of the camera even though the components are directly subjected to the fluid. This

11 11

6. Principle axis

7. Single, thin, convex lens

8. Focal point

9. Distance from object to lens

10. Distance from lens to image plane

11. Distance from object to image plane

9 10

1. Viewing angle

2. Pinhole aperture diameter

3. Aperture substrate thickness

4. Image plane

5. Focal length

5 5

8

8

7 6

4

(a)

1

5

4

2

3

(b)

36

direct immersion allows for pressure resistant design, without the need for a housing; thereby

also allowing for direct optical observation.

3.7. Challenges Encountered

The design of the optical and mechanical components of a camera system that was used

to monitor triaxial specimens from within a triaxial cell, submerged in confining fluid, and

subjected to high pressures is presented herein. The following challenges were encountered and

are addressed sequentially: (1) physical space requirements of placing multiple cameras within a

standard triaxial cell, (2) direct contact between electronic components of the camera and the

confining fluid, (3) space requirements for developing the appropriate focal length, (4) high cell

pressures during testing, (5) sufficient coverage of entire specimen area with minimal camera

deployment, and (6) analog to digital signal conversion for capturing still frames from video

feeds. Discoveries were made through an initial empirical trial and error process, and through

theoretical deductions to test, optimize, and fabricate new BCPA designs. The process that was

followed to address each of the interrelated challenges is presented in Figure 3.2. Specifically, of

most importance was the focal length, as the focal length was a function of all of the other

challenges. Each of the aforementioned challenges is further discussed in the forthcoming

sections.

37

Figure 3.2. The process that was followed to address the interrelated challenges in the

design of the BCPA.

3.7.1. Space Requirements

The first challenge was the small size of the triaxial cell (11.43 cm (4.5 in.)) inside

diameter Trautwein Soil Testing Equipment Co. triaxial cell). Only 3.81 cm (1.5 in.) of space

surrounded the 3.81 cm (1.5 in.) diameter specimen. To overcome this challenge, small closed

circuit board cameras (with dimensions of 14mm (0.55 in.)) by 14mm (0.55 in.) by 13mm (0.51

in.)) were placed into the cell in between the cell wall and the soil specimen. Several types of

cameras were investigated including various types of cameras with a 6.35mm (0.25 in.) format or

8.38mm (0.33 in.) format charge-coupled device (CCD) or complementary metal oxide

semiconductor (CMOS) sensor that were mounted to a circuit board that housed composite video

(yellow), audio (white), and power (red, black) wire leads and enclosed within an aperture box

with a threaded lens mount assembly.

The quality and size of the images produced from the respective cameras was partially a

function of the sensor size; therefore, given the available options, a 8.38mm (0.33 in.) format

sensor was selected over similar 6.35mm (0.25 in.) format sensors. Each of the cameras was

tested with a variety of standard lenses both in air and submerged in electronics-grade silicone

Space requirements (SR)

Confining fluid (CF)

Focal length (FL)

Cell pressure (CP)

Specimen coverage (SC)

Challenges Alternative Pursued

Small board cameras

Further challenges

PSF-5cSt silicone oil

Various lenses

Multiple cameras

Open body camera

Limited field of view

Refractive index of oil,

compressible air spaces

Solution

14x14x13mm (SR, SC)

Open body (CF, CP)

8 cameras (SC)

Rotating towers (SC)

BCPA

38

oil. Furthermore, only cameras with the highest lines of horizontal resolution (LoHR), and pixel

dimensions were selected (specifications ranged from 420 LoHR to 700 LoHR and 492 by 510 to

976 by 582, respectively). The board camera that was selected for use in the triaxial cell

possessed a 8.38mm (0.33 in.) format SONY CCD sensor, capable of obtaining 700 LoHR, and

976 horizontal by 582 vertical effective pixels. This camera was chosen because it had the best

image quality to size ratio, thereby facilitating deployment inside of the triaxial cell. Photographs

of the various types of cameras and lenses that were tested, and their respective specifications,

are presented in Figure 3.3.

Given the space constraints within the triaxial cell, it was not practical to design a lens

array to focus light for this application. It may have been possible to design a lens system to

improve the resolution of captured images; however, given the space constraints, the design

would have required using very small lenses (on the order of 2.0mm in diameter) with unusually

high refractive indices (greater than 1.8) to give the appropriate focal length when immersed in

the silicone oil. Specifically, the appropriate focal length that was required is discussed in the

section entitled focal length.

39

Figure 3.3. (a) Three types of board cameras that were tested, and (b) five different types of

lenses used with the cameras.

3.7.2. Confining Fluid

To avoid damage to the sensitive electronics of the cameras, while still ensuring

saturation of the specimen (by utilizing pressurized fluid instead of pressurized air to prevent gas

diffusion across the membrane), silicone fluid (PSF-5cSt, Trautwein Soil Testing Equipment

Co.) was used to confine the specimens and surrounded the cameras. Properties of the silicone

fluid include: low viscosity (5cSt), specific gravity of 0.918, dielectric constant of 2.60, dielectric

strength of 375, and index of refraction of 1.397. Due to the high refractive index of the oil

(relative to air), the standard lenses were not able to focus when immersed in the oil.

Specifically, the index of refraction of the silicone oil (1.397) was much greater than the index of

A

B

C

(a)

(b)

1 2 3

4

5

Board camera specifications:

A) 6.35mm [0.25in.] format Sharp

CCD sensor, 420 LoHR, 492×510,

M6.5×0.25 aperture box threading,

B) 8.38mm [0.33in.] format Sony


M12×0.5 aperture box threading;

C) 8.38mm [0.33in.] format Sony


M12×0.5 aperture box threading.

Lens specifications:

1) 3.6mm standard lens, 55° FOV;

2) 3.7mm button lens, 60° FOV;

3) 2.8mm barrel lens, 90° FOV;

4) 2.1mm wide angle lens, 170° FOV;

5) barrel-mounted pinhole aperture.

Note: All had M12×0.5 threading but

Lens 1 (M6.5×0.25 thread).

40

refraction of air (1.000 in a perfect vacuum). Although unknown, it was estimated that the index

of refraction of the lens material was between 1.48 and 1.60 (for crown or flint glass). The

increase in the index of refraction from 1.000 to 1.397 reduced the difference in the indices of

refraction between the two media (air–glass and oil–glass) and thereby increased the required

focal length. This reduction in the difference in the indices of refraction provided for non-ideal

light dispersion and therefore led to severely out-of focus images when the cameras containing

lenses were submerged in oil. Simply put, lenses were deemed to not be a viable option (as

discussed in further detail in the focal length section).

3.7.3. Focal Length

As discussed previously, limited space was available to deploy the cameras. This space

constraint limited the maximum achievable focal length (the distance between the object and the

lens, as shown in the ray diagram that was previously presented in Figure 3.1). The minimum

focal length values, for the standard lenses that were included with purchase of the board

cameras when tested in air, were between 4 and 6 cm (1.6 and 2.4 in.). These distances

corresponded to images with the highest sharpness; therefore, focused images could not be

obtained when using cameras with the standard lenses within the available confined space of

3.81 cm (1.5 in.). Furthermore, as revealed by submerging the cameras in the silicone oil, the

focal length of a given lens varied, depending on the medium that surrounded the lens.

Simply put, a camera lens designed to provide focus in air, did not provide focus in the

silicone oil. Although different types of lenses were tested (Figure 3.3), all of the lenses inhibited

viewing of soil specimens when the lenses were immersed in silicone oil. The testing of the

lenses was purely empirical, due to the unknown characteristics of the various lenses (lens shape,

refractive index of lens material, and radii of curvature of the lens surfaces). The characteristics

41

of the lenses were unknown because the small lenses were cemented and sealed inside of a

mounting assembly, making it impractical to extract the lenses or lens components for closer

inspection. The Lensmaker’s equation (previously presented as Equation 3.1) was employed to

determine the optical properties of a lens that would enable collection of images when immersed

in silicone oil. However, given the immersion medium, it was not economically, nor practically

feasible to purchase or (manufacture) a lens, or lens array, with the correct refractive index

(greater than 1.8) to develop the appropriate focal length (approximately 24mm (0.94 in.)) within

the physical space limitations (3.81 cm (1.5 in.)). Therefore, as discussed in the section entitled

Pinhole Solution, another solution was realized to enable collection of images from close

distances within a fluid with a high refractive index.

3.7.4. Cell Pressure

To withstand the cell pressures during testing (up to 1034 kPa (150 psi)), the cameras

were flooded behind the aperture, filling all of the air space with oil. It was observed, in original

testing of the lensed cameras, that the focal length of the lens arrays permanently changed after

being subjected to typical pressures. This was attributed to the compression of the small void

spaces between the lenses when subjected to pressure, resulting in permanent deformation of the

lenses and thereby altering the optical properties of the lens array. It was therefore determined

that an alternative to a lens array must be developed to withstand pressure applications.

3.7.5. Specimen Coverage

Due to the close proximity of the board camera to the soil specimen, it was not possible

to observe the entirety of the specimen with a single camera. Specifically, the field of view of an

individual camera (21mm (0.83 in.)) was smaller than the height of the specimen (7.62 cm (3.0

in.)). Therefore, by using multiple cameras, individual areas of the specimen were monitored and

42

the photographs of the individual areas were stitched together using post-processing software. To

achieve this, a camera monitoring system was designed with two arrays of four BCPA (eight

total cameras). The BCPAs were mounted to towers that were rotated along a track that was

attached to the base inside of the cell. The track was designed to rotate using pairs of small

magnets; one magnet was mounted to the track and the other magnet was located at various

positions outside of the triaxial cell wall. The use of magnets allowed for the BCPAs to capture

still frames at prescribed intervals during the rotation. A schematic of the track and camera tower

system is presented in Figure 3.4.

Figure 3.4. Schematic of guided camera track system mounted on triaxial apparatus base.

6. Camera cable

7. Rotating Delrin® bearing track

8. Delrin® bearing base

9. Magnet

10. Triaxial apparatus base

8

9

3

4

7

1. BCPA (typical, 8 quantity)

2. Soil sample

3. Camera tower

4. Acrylic top cap

5. Drain lines

1

2

5

5

10

6

5

43

In the original design of the cameras, it was hypothesized that using wide-angle lenses

would be sufficient to capture large areas of the specimen and, therefore, very few cameras

would be required. However, the use of this type of lens was not permitted (due to the

aforementioned problems associated with lenses not enabling image collection when submerged

in silicon oil, due to the physical size requirements of the lenses, and due to the distortions that

were associated with wide-angle lenses (barrel, pincushion, and complex distortions)). Although

these distortions are now a moot point because the wide-angle lens could not be used, these

distortions are known to be difficult to correct and typically reduce the size of the image (due to

cropping requirements).

3.8. Pinhole Solution

To overcome the limitations of focal length, refractive properties of the confining fluid,

cell pressure, and specimen coverage, a lensless pinhole aperture was developed. The required

aperture diameter was approximated, based on Equation 3.2 (Strutt 1891):

𝑓 = 2𝑟2/𝜆 Strutt (1891) Equation 3.2

Where f is the focal length, r is the radius of the pinhole opening (or aperture), and λ is the

design wavelength.

However, unlike for a lens, the f variable used in Equation 3.2 was associated with the

distance between the pinhole aperture and the camera sensor plane, as previously depicted in

Figure 3.1. Furthermore, as discussed previously, unlike lensed cameras, pinhole cameras have

infinite depth of field; therefore, this type of aperture allowed for the entire image to be in focus.

To obtain sharp images and to maximize resolution, the edges of the pinhole must be precisely

cut and the diameter of the pinhole must be small. Moreover, the thickness of the substrate must

be thin to allow for the widest viewing angle (as shown previously in Figure 3.1). Therefore,

44

various pinhole sizes 75, 100, and 150 μm (2.95×10-3, 3.94×10-3, and 5.91×10-3 in.) were laser

cut into the center of a 9.5mm (0.375 in.) diameter wafer substrate (National Aperture, Part

Number 1-75+ B-2, 1-100+ B-2, and 1-150+ B-2), respectively. The steel substrate (300 series

stainless steel) had a thickness of 12.7 μm (5×10-4 in.) and both sides were blackened (+B-2) to

absorb any stray light within the aperture box.

The design optical wavelength (415 nm) was selected based on the results obtained from

a relative light intensity test that was conducted by examining a diffuse reflectance

fluoropolymer reference material (Spectralon, Labsphere, Inc.) using a spectroradiometer (ASD

FieldSpec Pro HandHeld 2 portable spectroradiometer). Although a peak value of 580nm was

observed, a reduced value of 415nm was utilized because of the refractive index ratio (1.397)

that was associated with silicone oil being used as the confining fluid instead of air. Furthermore,

this wavelength (415 nm) was selected because the final position of the pinhole aperture was

fine-tuned (in relation to the camera image plane) using a threaded barrel that screwed into the

aperture box.

A recess was placed into the threaded barrel to enable the wafer substrate to be mounted

to the barrel. The aforementioned three aperture diameters were tested at various distances from

the camera sensor, and it was found that the 75 μm (3.94×10-3 in.) diameter aperture provided

the best image quality when the substrate was located approximately 3.0mm away from the

image plane, as assessed by visual inspection of the acquired images. Therefore, the final design

components of the BCPAs are thus: (1) an 8.38mm (0.33 in.) format board camera encased in an

aperture box with a M12×0.5 threaded opening; (2) a threaded barrel that was used for seating

and adjusting the pinhole aperture substrate; and (3) a laser cut pinhole aperture (75 μm

opening), centered at a specified focal length (3.0 mm) from the camera sensor. A schematic and

45

4. Aperture box

5. Video signal and power supply cable

6. CCD sensor (5.0mm × 4.8mm)

1. Pinhole aperture (75μm diameter)

2. Pinhole substrate (9.5mm diameter, 12.7μm thick)

3. Threaded barrel (M12×0.5, 6.5mm inside diameter)

1. Substrate (9.5mm diameter) with pinhole (75μm

diameter)

2. Threaded barrel (M12×0.5, 6.5mm inside diameter)

3. Aperture box

4. Video signal and power supply cable

a photograph of the assembled BCPA are presented in Figures 3.5 and 3.6, respectively. As

discussed in the section entitled images collected, the BPCA design and fabrication enabled

images to be collected from inside of the triaxial cell while the cameras were immersed in

silicone oil and subjected to high pressures.

Figure 3.5. Schematic of (a) front view, (b) exploded side view, and (c) exploded orthogonal

view of the BCPA.

Figure 3.6. Photograph of one of the BCPAs utilized inside of the triaxial cell.

3.0 mm

9.5 mm

3.0 mm

6.5 mm

14.0 mm

(a)

1

(b) (c)

14

.0 m

m

13.0

mm

2

2

1.0 mm

3

4

5

6

5

6

1

2

4 3

46

3.8.1. Video Signal Acquisition

The video cables of the cameras were connected to a wire harness that was connected to a

nine-pin feedthrough connector located within the top cap of the triaxial device. The feedthrough

allowed for electrical signals to travel into and out of the triaxial device. The video wires that

were connected to the cameras were also connected to the pins on the nine-pin feedthrough

connector; the opposite sides of the pins were connected to the input channels of an eight-way

video/audio switch (Maituo MT-VIKI 8 Port VGA Switch). The single video output channel

from the video/audio switch was then connected to a Universal Serial Bus 2.0 Digital Video

Adapter (Sabrent USB-AVCPT). Each camera was supplied with external power (DC 12V) from

a common external power supply (Enercell 3-12VDC 1A AC Adapter) that provided power to all

of the cameras simultaneously via the nine-pin feedthrough connector. The video feed from each

of the cameras was subsequently received and displayed by switching the video/audio switch.

The software that was included with the video adapter (Sabrent USB 2.0 Video Capture Creator

with Audio) was utilized to capture still frames from the video feed that was obtained from each

of the cameras.

3.9. Images Collected

Still frames, captured from the video feed of a board camera with a lens (located in air

and immersed within PSF-5cSt silicone oil), are presented in Figures 3.7(a) and 3.7(b),

respectively. Still frames, captured with the BCPA (located in air and immersed within PSF-5cSt

silicone oil), are presented in Figures 3.7(c) and 5.7(d), respectively. An example of linear

distortion in images captured using a lens is evident in Figure 3.7(a) and the inability of the

camera to collect focused light through the lens to form a real image is displayed in Figure

3.7(b). As explained previously, because the lens was designed to work in air, the index of

47

refraction of the silicone oil prevented the camera that was fully immersed within oil from

obtaining a focused image.

Figure 3.7. Still frames captured using a 8.38mm [0.33in.] format CCD board camera with

1) 3.7mm button lens (55° FOV, M12×0.5 thread) in (a) air, and within (b) PSF-5cSt

silicone oil, and with 2) 75μm diameter pinhole aperture (attached to a M12×0.5 barrel

with 6.5mm diameter opening) in (c) air, and within (d) PSF-5cSt silicone oil.

It was determined that the captured light on the far left and far right edges of the images

collected using the BCPA faded abruptly and completely (as indicated by the areas to the left and

right of the dashed white lines in Figures 3.7(c) and 3.7(d)). This phenomenon was attributed to a

combination of physical and optical influences. The aperture barrel material blocked the edges of

the CCD sensor along the longer (horizontal) side of the CCD sensor (due to the proximity of the

barrel to the sensor). Thereby, light was prevented from reaching the edges of the CCD sensor

that led to the black appearance. Although not required, the proximity limitation should be

(a) (c)

(d) (b)

48

overcome by enlarging the inside diameter of the threaded barrel. However, it was determined

that, given the experimental equipment, the dimensions of the shorter (vertical) side of the sensor

provided sufficient coverage of the object (if the camera was rotated in such a way that the

camera cable exited from the camera in the horizontal plane as shown previously in Figure 3.4)

and therefore an increase in the inside diameter of the barrel was not necessary. Furthermore, the

“airy disk” covered the entire camera sensor so no visible diffraction patterns were present.

As observed in the comparison between images captured with a lens and those captured

with a pinhole aperture, there was a significant difference in the amount of light exposure. The

lens (Figures 3.7(a) and 3.7(b)) allowed for maximum light gathering. The pinhole aperture

(Figures 3.7(c) and 3.7(d)) allowed for minimal light entry, due to the small size of the opening

(75 μm (3.94×10-3 in.) diameter). In typical pinhole photography, this minimal amount of light

entry is commonly overcome with longer exposure times; however, for the type of board camera

that was used, it was not possible to control the exact exposure time (electronic shutter time

varied between 1/60 and 1/100 000 s, as per the camera manufacturer). Furthermore, the board

camera switched into “night mode” (monochromatic light gathering) when the illuminance levels

dropped below a certain threshold (0.1 lux). Chromatic aberration may have been present in the

captured images, but it was not possible to detect this type of aberration due to the

monochromatic nature of the images. Although the lighting was not modified to collect the

images presented in Figure 3.7, it is recommended that the lighting surrounding the soil sample

be enhanced and controlled to aid in collection of higher quality imagery. Specifically, utilizing

two 17.8 cm (7 in.) diameter dome light sources to surround the entire triaxial chamber will

enhance the imagery. With the aid of the guided camera track system, multiple still frames were

captured with the individual BCPAs along the length of the soil specimen, at prescribed intervals

49

during rotation around the circumference of the specimen. Because of the overlapping fields of

view of adjacent BCPAs, in the vertical direction and in circumferential direction, common

points were acquired within captured images, and the individual geopositions of the cameras

were calculated, allowing for post-process stitching of the collected images. PhotoModeler (Eos

Systems, Inc. 2014) was utilized to calculate the photogrammetric properties of the BCPA (Table

3.1). These properties included the focal length, format size (physical dimensions of the sensor)

and principal point (intersection between principal axis and image sensor). PhotoModeler was

also used to determine the geoposition of each of the individual BCPAs. Specifically, the

positions of the BCPAs were determined by using unique, pre-selected targets that were adhered

to a 1.5 in. (38mm) diameter by 3 in. (76mm) tall brass specimen and that were automatically

recognized within the software. The PhotoModeler obtained photogrammetric properties and

geopositions corresponded well with manual (caliper) measurements.

Table 3.1. Photogrammetric properties of the BCPA.

Focal length (mm) Format size (mm) Principal point (pixels)

3.50 5.16 width 2.62 x

4.80 height 2.23 y

Using repeatable rotation intervals, and therefore known geopositions of each of the

individual BCPAs, PhotoModeler was used to match common points within the captured images

that thus enabled generation of a point cloud for any object that was viewed by the BCPAs. This

point cloud was then meshed to calculate the dimensions and volume of the viewed object. By

utilizing this experimental method (PhotoModeler), the volume of the brass specimen that was

obtained was 91.92 cm3. The volume obtained using manual (caliper, pi tape) measurements was

91.93 cm3, resulting in an estimated error of 0.01 %.

50

3.10. Conclusions

A small board camera with a pinhole aperture was designed for deployment inside of a

triaxial cell to enable measurement of the volume of soil specimens. Because the camera

components were fully immersed in oil and were located very close to the soil specimen, special

considerations were accounted for when designing the optical components of the

photogrammetric instrumentation. To resist the high pressures that are commonly encountered

within the triaxial cell during triaxial testing (up to 1034 kPa (150 psi)), the silicone oil was

allowed to enter behind the camera face and to surround the CCD sensor. The relatively high

refractive index of silicone oil (as compared to the refractive index of air) influenced the light

entering into the traditional lenses or lens arrays yielding severely out of focus images (because

the refractive index of the lens or lens array closely matched the refractive index of the lens

confining fluid).

Utilizing the Lensmaker’s equation, it would have only been possible to focus an image

using small lenses with unusually high refractive indices. However, this option was not pursued

because it was (1) limited by availability, (2) costprohibitive, and (3) required the design and

fabrication of additional lens mounts and boxes. Instead, the as provided lens that was located

within the aperture box of each of the board cameras was replaced with a newly created high-

precision pinhole aperture. The pinhole cameras were designed, fabricated, tested, and their

potential applicability inside of a triaxial cell evaluated. Specifically, high quality images were

acquired using the BCPA even when the BCPA was placed inside of the triaxial cell, immersed

in silicone oil, and subjected to high pressures. Furthermore, a guided track system was designed

to allow for coverage of the entire soil specimen, while deploying the minimal number of BCPAs

within the triaxial cell.

51

3.10.1. Advantages and Limitations of a BCPA

In summary, a careful balance existed between resolution, light entry, and field of view.

To truly optimize the design of the camera, it was necessary to experiment with a variety of

different pinhole diameters and focal lengths. There are many advantages to BCPAs, two of

which are an infinite depth of field (including very close depths) and a lack of any of the optical

aberrations associated with lenses. Other advantages of using a pinhole-type camera are as

follows: the BPCA: (1) is not adversely affected by the refractive properties of the immersion

fluid (silicone oil); (2) requires very little space to develop appropriate focal length and requires

less space than a lens or lens array; (3) may be designed to provide very large viewing angles

without the need for a lens; and (4) can withstand pressure. The disadvantages are primarily low

light entry and limited resolution; however, with proper design and fabrication, these

disadvantages were overcome. By utilizing a BCPA, images were obtained within a triaxial cell

even though the optical design of the BCPA was simplified from that of a traditional lensed

camera.

52

3.11. References

Airy, G. B., 1835, “On the Diffraction of an Object-Glass With Circular Aperture,” Trans.

Cambr. Philos. Soc., Vol. 5, pp. 283–291.



Alshibli, K. A. and Al-Hamdan, M., 2001, “Estimating Volume Change of Triaxial Soil

Specimens From Planar Images,” Comput-Aid. Infrastruct. Eng., Vol. 16, No. 6,

pp. 415–421.


Measurement System for Triaxial Tests,” Geotech. Test. J., Vol. 35, No. 2, pp. 1–18.

Eos Systems Inc., 2014, PhotoModeler (Version 2014.1.1). 3D Measurements and Models

Software, http://www.photomodeler.com/index.html (Last accessed 13 Oct 2014).

Fresnel, A.-J., 1819, “Memoir on the Diffraction of Light,” The Wave Theory of Light, H. Crew,

Trans., American Book Company, New York.



pp. 98–103.

Grimaldi, F. M., 1665, Physico–mathesis de lumine, coloribus, et iride, aliisque adnexis libri duo

[A physiomathematical thesis on light, colors, the rainbow and other related topics in two

books], Bologna, Italy (in Latin).

Hendriks, B. H. W., Kuiper, S., van As, M. A. J., Renders, C. A., and Tukker, T. W., 2006,

“Variable Liquid Lenses for Electronic Products,” Proc. SPIE, Vol. 6034, pp. 10–18.

Herschel, J. F. W., 1835, Treatise on Astronomy, 3rd ed., Carey, Lea & Blanchard,

Philadelphia, PA.

Kingslake, R. and Johnson, R. B., 2010, Lens Design Fundamentals, 2nd ed., Academic Press,

New York.

Kuiper, S. and Hendriks, B. H. W., 2004, “Variable-Focus Liquid Lens for Miniature Cameras,”

Appl. Phys. Lett., Vol. 85, No. 7, pp. 1128–1130.

Kuo, C.-H. and Ye, Z., 2004, “Sonic Crystal Lenses that Obey the Lensmaker’s Formula,”

J. Phys. D., Vol. 37, No. 15, pp. 2155–2159.

Lasance, C. and Simons, R., 2005, “Advances in High Performance Cooling for Electronics,”

Electron. Cool., Vol. 11, No. 4, pp. 22–39.

53

Laudo, J. S., Wurm, K., and Dodson, C., 1998, “Liquid-Filled Underwater Camera Lens

System,” Proc. SPIE, Vol. 3482, pp. 698–702.



pp. 103–109.

Mahajan, V. N., 1998, Optical Imaging and Aberrations: Part I. Ray Geometrical Optics, SPIE,

Bellingham, WA.

Mohapatra, S. C. and Loikits, D., 2005, “Advances in Liquid Coolant Technologies for

Electronics Cooling,” Proceedings of the 21st IEEE Semiconductor Thermal

Measurement and Management Symposium, San Jose, CA, March 15–17, pp. 354–360.

Newton, I., 1730, Opticks: Or a Treatise of the Reflections, Refractions, Inflections and Colours

of Light, 4th ed., William Innys, London.

Nguyen, N.-T., 2010, “Micro-Optofluidic Lenses: A Review,” Biomicrofluidics, Vol. 4, No. 3,

031501.

Parker, J. K., 1987, “Image Processing and Analysis for the Mechanics of Granular Materials

Experiment,” ASME Proceedings of the 19th SE Symposium on System Theory, ASME,

New York, pp. 536–541.

Renner, E., 2000, Pinhole Photography: Rediscovering a Historic Technique, 2nd ed.,

Butterworth–Heinemann, Boston, MA.

Roichman, Y., Waldron, A., Gardel, E., and Grier, D. G., 2006, “Optical Traps with Geometric

Aberrations,” Appl. Opt., Vol. 45, No. 15, pp. 3425–3429.


Using Digital Image Analysis (DIA) Technique,” Soils Found., Vol. 47, No. 1,

pp. 67–78.

Salazar, S. E. and Coffman, R. A., 2014, “Design and Fabrication of End Platens for Acquisition

of Small-Strain Piezoelectric Measurements During Large-Strain Triaxial Extension and

Triaxial Compression Testing,” Geotech. Test. J., Vol. 37, No. 6, pp. 948–958.

Schmidt, R., 2005, “Liquid Cooling is Back,” Electron. Cool., Vol. 11, No. 3, pp. 34–38.

Strutt, J. W., Lord Rayleigh, 1891, “On Pin-Hole Photography,” Philos. Mag., Vol. 31,

pp. 87–99.

Young, T., 1802, “Bakerian Lecture: On the Theory of Light and Colours,” Philos. Trans. R.

Soc. Lond., Vol. 92, pp. 12–48.

54

Young, M., 1971, “Pinhole Optics,” Appl. Opt., Vol. 10, No. 12, pp. 2763–2767.

55

CHAPTER 4: DEVELOPMENT OF AN INTERNAL CAMERA-BASED VOLUME

DETERMINATION SYSTEM FOR TRIAXIAL TESTING


The development of the internal camera-based volume determination system is described

in this chapter. The instrumentation presented within this manuscript provided a novel alternative

to the state-of-the-art of camera-based monitoring of triaxial tests. The individual components of

the system, the photogrammetric methodology, and preliminary testing of the system are

detailed.

The limitations of the included manuscript (Salazar et al. 2015) are discussed in


background for the manuscript are described in Sections 4.4, 4.5, and 4.6. Contained within

Section 4.7 is a detailed description of the camera system, including the mechanical and

electrical components of the system (Sections 4.7.1 and 4.7.2, respectively). The

photogrammetric methodology and early results are detailed in Section 4.8. Finally, conclusions

for this manuscript are presented in Section 4.9.


The manuscript contained within this chapter was originally published as a technical note

in order to follow up the Salazar and Coffman (2015) publication that first introduced the

internal camera-based volume determination system. The length of the manuscript was therefore

limited. Although the preliminary testing of the system was described as a "validation process",

the tests did not include any triaxial tests on soil specimens, nor were the camera-based

measurements subject to immersion in confining fluid (all tests were performed in an air-filled

cell only). Furthermore, the photogrammetric methodology that was utilized to determine the

56

volume of a dummy specimen within the testing cell was described in broad terms, but an

overview of the implementation of the system was provided.

4.3. Development of an Internal Camera-Based Volume Determination System for Triaxial

Testing

Reference

Salazar, Sean E., Barnes, Adam, and Coffman, Richard A., “Development of an Internal

Camera-Based Volume Determination System for Triaxial Testing,” Geotechnical Testing

Journal, Vol. 38, No. 4, 2015, pp. 549-555. doi:10.1520/GTJ20140249.

4.4. Abstract

A triaxial testing cell was instrumented with an internal camera monitoring system. By

placing the camera monitoring system inside of the triaxial cell, optical distortions due to

refraction at the confining fluid–cell wall and cell wall–atmosphere interfaces and the

curvature of the cell wall were eliminated. The components of the system are presented.

Furthermore, the photogrammetric techniques that were utilized to analyze the

photographs that were captured from within the triaxial cell are discussed. The proposed

methods for acquiring and analyzing the photographs are presented and the potential for

the inclusion of an internal camera–monitoring system for triaxial testing applications are

discussed.

Keywords: triaxial testing, laboratory equipment, photogrammetry

4.5. Introduction

Of the unconventional testing methods (photogrammetry, other digital imaging

techniques, proximity sensors, x-ray-computed tomography) used to monitor saturated and

unsaturated soil specimens during triaxial testing, photograph-based measurement is a practical,

cost-effective, and versatile method. Photogrammetry may be utilized to: (1) characterize the

failure plane within a soil specimen during testing, (2) monitor the critical cross-sectional area of

57

the soil specimen (bulging or necking behavior), (3) calculate the volume of the soil specimen,

and (4) calculate the volumetric strain within the soil specimen. Several drawbacks exist with

current photograph-based instrumentation, namely the optical effects caused by the curvature of

the cell wall, refraction at the confining fluid–cell wall and cell wall–atmosphere interfaces, and

optical distortions inherent to lensed cameras. These drawbacks must be overcome and corrected

using cumbersome models, further complicating the procedure of acquiring and processing

images.

As described in Salazar and Coffman (2015), the optical components of internal

photogrammetric instrumentation (cameras located within the cell fluid on the inside of the

triaxial cell) for triaxial testing applications were designed, fabricated, and tested to overcome

the aforementioned drawbacks, as well as to overcome the challenges of internal instrumentation

(space, confining fluid, focal length, cell pressure, and specimen coverage). Details about the

photogrammetric system that was placed within the triaxial cell to allow for direct, unobstructed

observation of a specimen during triaxial testing are presented herein. The system allowed for

viewing of the entire specimen surface in both the axial and radial directions. Calibration and

validation of the system was attained by utilizing a photogrammetric technique to digitally

reconstruct the exterior shape of a specimen with known dimensions. The methodology that was

employed to reconstruct the exterior surface and the accuracy and precision of the

photogrammetric measurements are presented and discussed for completeness.

4.6. Background

Specimen volume and volumetric strain measurements have historically been calculated

for soil specimens, during triaxial testing, by utilizing pore fluid volume measurements (Bishop

and Donald 1961, Ng et al. 2002, Leong et al. 2004). These pore fluid measurements have

58

typically been supplemented with data obtained from axial deformation measurements to obtain

the average specimen dimensions, during or after testing, by adding or subtracting the

measurements from the dimensions of the specimen that were manually measured (caliper and pi

tape) prior to testing. Because the volume measurements have been attained by measuring the

change in the amount of pore fluid, the measurements have been affected by temperature- and

pressure-induced flexure of the cell wall and drain lines. Therefore, only estimates, not exact

values, of volumetric strain have been obtained from these measurements. Likewise,

conventional axial (Scholey et al. 1995, Cuccovillo and Coop 1997, Ng and Chiu 2001) and

lateral or radial (Khan and Hoag 1979, Clayton et al. 1989, Bésuelle and Desrues 2001)

measurements also rely on averaging methods that have not accurately accounted for irregular

surfaces. Furthermore, past measurements have been limited to global volume changes that

prevented the characterization of local strains during the development of shear bands, bulging

bifurcation, or, in the case of extension testing, necking.

To overcome these limitations, digital imaging techniques, including digital image

analysis (DIA), digital image correlation (DIC), and particle image velocimetry (PIV), have been

used to monitor deformations within soil specimens by using external (cameras located outside

of the triaxial cell) cameras. Specifically, these techniques have been of increasing interest as an

alternative method to calculate the volumetric strain of soil specimens (Macari et al. 1997,

Alshibli and Al-Hamdan 2001, Puppala et al. 2004, Rechenmacher and Finno 2004, Ören et al.

2006, Gachet et al. 2007, Sachan and Penumadu 2007, Önal et al. 2008, Bhandari et al. 2012)

and to monitor the evolution of shear banding and strain localization (Alshibli and Sture 1999,

Nübel and Weitbrecht 2002, Gudehus and Nübel 2004, Rechenmacher and Medina-Cetina 2007,

Sachan and Penumadu 2007). Photograph-based (DIA, DIC, PIV, photogrammetry)

59

measurements have been shown to correlate well with conventional volume measurements of the

soil specimen within the triaxial apparatus during testing (Macari et al. 1997, Alshibli and Sture

1999, Alshibli and Al-Hamdan 2001, Gachet et al. 2007, Rechenmacher and Medina-Cetina

2007, Sachan and Penumadu 2007, Bhandari et al. 2012, Zhang et al. 2015).

Video feeds and/or still frames of the soil specimens, within the triaxial device, were

captured with external photographic equipment in all of the aforementioned photograph-based

measurement studies. For volumetric measurements, the external instrumentation allowed for

capture of the entire length of the specimen (axial dimension) within a single image; however,

various methods were employed to capture the entire surface area (lateral dimension) of the

specimen. These methods included the use of multiple cameras placed at intervals around the

outside of the cell (Alshibli and Al-Hamdan 2001, Bhandari et al. 2012). In some instances

(Macari et al. 1997, Gachet et al. 2007), the entire specimen surface was not captured and,

therefore, it was not possible to capture all of the surface irregularities by assuming specimen

symmetry. In other instances (Liang et al. 1997, Alshibli and Sture 1999, Sachan and Penumadu

2007), the entire specimen surface was not captured because only the zone of shear banding

within soil specimens was investigated and volumetric measurements of the entire specimen

were not obtained. Because all of these previous methods utilized external cameras, several

optical challenges were encountered, as described in detail in Bhandari et al. (2012). Zhang et al.

(2015) presented the first true photogrammetric local and total volume measurements of a

triaxial specimen. As stated in Zhang et al. (2015), the need for photogrammetry was based on

the significant limitations and unrealistic assumptions of other photograph-based measurement

methods (i.e., only local volume was obtained; accurate and precise control of relative camera

location and camera orientation were required). Although the Zhang et al. (2015) method

60

overcame the limitations of many other photograph-based methods, the Zhang et al. (2015)

method still required computationally intensive ray tracing and least-squares optimization to

correct for the curvature of the cell wall, for the deformation of the cell under cell pressure, and

for light refraction at the confining fluid–cell wall and cell wall–atmosphere interfaces.

4.7. Internal Camera-Monitoring System

As described in Salazar and Coffman (2015), a small board camera with a pinhole

aperture (BCPA) device was developed to acquire photographs from within the triaxial cell. The

various challenges of utilizing internal photogrammetric instrumentation, namely, space

requirements, confining fluid, focal length, cell pressure, and specimen coverage, were overcome

by developing and utilizing the BCPAs. The optical, mechanical, and electrical components were

considered in the design of the BCPA device and combined BCPA system. Specifically, the

optical components were presented in Salazar and Coffman (2015), whereas the mechanical and

electrical components are presented herein. A schematic of the components of the combined

BCPA-monitoring system is presented in Figure 4.1.

61

Figure 4.1. (a) Exploded view, and (b) elevation view of the internal components of the

combined BCPA monitoring system.

4.7.1. Mechanical Design

Multiple BCPA devices were employed to enable photographic coverage of the entire

surface of the specimen (during consolidation and shearing up to 15 % axial strain in triaxial

compression or triaxial extension). Given the vertical viewing angle of each of the individual

BCPAs (approximately 73º), the BCPA devices were stacked to allow for overlapping fields

of view along the length of the specimen in the axial direction. To minimize the required

number of BCPAs, a rotating platform was designed and fabricated to allow for several

overlapping images at each point around the specimen in the radial direction. Because of

the presence of two diametrically opposed vertical drain lines within the triaxial cell, which

enable drainage from the top of the specimen through the top platen, a full 360º revolution of

a single BCPA tower was not possible. Therefore, two diametrically opposed BCPA towers

4

7. Delrin® top guide

8. Tab for BCPA tower

9. Rotating Delrin®

bearing track

10. Delrin® base

11. Triaxial base

12. Cell wall

6

3

1. Drainage lines

2. Individual BCPA

device (10 total)

3. Acrylic cap (2 total)

4. BCPA tower

5. Soil specimen

6. Internal magnet

7

2

(a)

5

(b)

11

10

9 8

1

12

62

were required, and the towers were rotated between the two drain lines. Each tower

rotated with 155º of rotation. Given the horizontal fields of view of the individual BCPA

devices and the required image overlap for photogrammetric processing, the towers were

rotated around the specimen and the towers were stopped at a desired degree interval to

acquire images.

To facilitate smooth and precise rotation of the two BCPA towers around the soil

specimen, the rotating platform utilized a stiff, low-friction, thermoplastic material

[polyoxymethylene (Delrin)], and an L-shaped slot design. A 25.4 mm x 25.4 mm x 12.7 mm

[1 in. x 1 in. x 0.5 in.] neodymium magnet (52 MGOe) located on the outside of the cell was

circumferentially rotated around the outside of the cell wall to pull a 6.35-mm [0.25-in.]

diameter neodymium magnet, which was mounted to the base of one of the BCPA towers,

causing the towers to rotate circumferentially around the vertical axis.

4.7.2. Electrical Design

Signals were passed into and out of the triaxial cell through the top cap of the cell by

utilizing a pinned throughput connector (as previously described in Salazar and Coffman

2014). Video, power, and ground wires were connected in such a way as to reduce the

required number of pin connections because of the large number of BCPA devices that were

employed (ten). The video and ground wires from each of the BCPA towers were connected

to common outputs, and the power wires from each BCPA were connected to a power control

switchboard (Figure 4.2), which allowed for only one BCPA to be powered at a given time

(thereby avoiding any video output feedback through the common grounding). Power was

individually supplied to each of the BCPA devices by increasing the amount of current that was

supplied to each transistor on the switchboard. Specifically, power was supplied to a given

63

1. Capacitor (200 V, 100 μF)

2. Standard timer

3. Voltage regulator (1.2-37 V)

4. Power (BCPA devices, 3.7 V)

5. Transistors (222 A)

6. Sequencing counter (650 ns)

7. Capacitor (50 V, 10 μF)

8. Common ground

9. Power (switchboard, 6.0 V)

10. Variable resistor (timing, 10-20 sec.)

BCPA when the amount of current matched a given transistor. The user then acquired still

frames from the video feed when a desired BCPA device was powered. The power to the

switchboard was supplied via an AC to DC converter (6 V; maximum 1 A). The voltage

regulators on the switchboard conditioned the power to the requisite level (3.7 V) for the BCPA

devices. The video feed was collected using a desktop computer via a USB interface video

adapter (Sabrent USB-AVCPT). The still frames were captured and stored by utilizing video

software (Ulead VideoStudio). A wiring diagram of the entire data collection system is presented

in Figure 4.3.

Figure 4.2. Photograph of the power switch board for the BCPA devices (power supply and

timing sequence).

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t

h

a

t

s

u

r

r

o

u

To BCPA devices

To throughput

connector

64

Figure 4.3. Wiring diagram of the photogrammetric instrumentation.

4.8. Photogrammetric Methods and Results

The following process (Figure 4.4) was utilized to calibrate and validate the camera

monitoring system and to reconstruct a digital three-dimensional model of a brass test specimen

with nominal dimensions of 3.81 cm (1.5 in.) in diameter by 7.62 cm (3.0 in.) in length. (1) Each

BCPA device was calibrated by capturing a series of images of a printed PhotoModeler

Computer and image

acquisition program

Throughput pin connector

Universal serial bus

(USB) video adapter

Switchboard

Direct current

power supply to

switchboard and

BCPA devices

RCA video

connector

Video signal

BCPA devices/towers

Common ground splice

Power (BCPA devices)

Ground

(BCPA devices)

65

calibration grid. The images of the calibration grid were subsequently analyzed using the

PhotoModeler Scanner software (PhotoModeler Scanner 2015) to obtain the necessary intrinsic

camera parameters (focal length, sensor format size, and principal point) of the BCPA. (2)

PhotoModeler coded targets [ringed automatically detected (RAD)] were adhered to the side of

the aforementioned brass specimen, and the specimen was placed on a flat surface where

additional RAD targets were adhered to the surface on which the specimen rested (96 targets

total). A previously calibrated digital single lens reflex (DSLR) camera (Canon 5D Mark II with

fixed 28mm Nikkor lens) with known properties (aperture controlled, f/13, ISO 1250, 28mm

fixed lens, and as calibrated using a PhotoModeler calibration grid) was used to capture images

of all sides of the specimen. Each RAD target was captured in a minimum of four images. (3)

The DSLR-acquired images were processed using the PhotoModeler software, and the center of

each target was precisely surveyed to within 0.2mm (0.0079 in.). (4) The same brass specimen,

with the same adhered targets, was then placed within the triaxial cell, and the target-covered

surface was captured using the BCPA devices that were mounted on the two towers. Five-degree

intervals were utilized to acquire a total of 320 images. As shown in Figure 4.5, adjacent images

were overlapped in both the axial and radial directions. (5) The common control points within

the DSLR and the BCPA images (see a12, b21, c32 in Figure 4.5) were used to

photogrammetrically derive the location and orientation of each of the individual BCPA devices,

at a given rotation interval, within the cell.

66

Figure 4.4. (a) PhotoModeler camera calibration grid, (b) DSLR-acquired survey images

(control point identification), (c) BCPA-acquired calibration images (camera location and

orientation identification), and (d) BCPA-acquired images (point cloud identification).

Figure 4.5. Vertically and horizontally overlapping photographs captured with two

adjacent BCPA on a single tower at 15 degree rotation intervals.

a12

b21

a12 a12

b21

b21 b21

c32

c32

67

To determine the practical range of rotation intervals (number of stations during rotation),

specific sets of the captured images were removed from the total 320 images (as captured from

the 5º rotation interval). Specifically, the locations and orientations of BCPA devices were

derived by using different intervals (45º, 30º, 15º, and 5º rotation intervals). Three-dimensional

recreations from the PhotoModeler software, of the calibration specimen surface (control points)

and BCPA device locations and orientations within the triaxial cell, are shown in Figure 4.6.

Photographic measurements obtained from the software, based on the DSLR survey, were

utilized to calculate a volume for the brass test specimen. A volume of 91.58 cm3 was obtained,

which corresponded to an estimated difference of 0.34 % when compared to the volume

calculations that were obtained from manual measurements (caliper and pi tape). Given

repeatable positioning of the BCPA towers at a desired rotation interval, the derived location and

orientation values for the individual BCPA devices were able to be used, in conjunction with

PhotoModeler software, to measure points on the surface at any axial strain level, for any soil

specimen that was tested within the triaxial cell. The measured points resulted in a point cloud

that was then used to identify the surfaces of the given specimen. The point cloud was then

exported from PhotoModeler Scanner and imported into Geomagic Design 3D software

(Geomagic Design X 2015) to obtain accurate threedimensional reconstructions of any specimen.

68

Control point obtained from DSLR survey, used to identify the locations of the BCPA devices

Photograph from BCPA device location/rotation

Figure 4.6. Photogrammetric reconstruction of BCPA device locations within the triaxial

cell for (a) 45 degree, (b) 30 degree, (c) 15 degree, and (d) 5 degree rotation intervals.

(a) (b)

(c) (d) Location of drain line

Location of drain line

69

4.9. Conclusions

Internal photogrammetric instrumentation was designed and implemented for triaxial

testing applications. The mechanical and electrical components of the BCPA instrumentation

were presented and the utilized photogrammetric techniques were discussed. The calibration and

validation processes for the system were also described. Based on preliminary findings, use of an

internal camera monitoring system is promising for future triaxial testing applications.

70

4.10. References

Alshibli, K. A. and Al-Hamdan, M. Z., 2001, “Estimating Volume Change of Triaxial Soil

Specimens From Planar Images,” Comput.-Aided Civil Inf. Eng., Vol. 16, No. 6,

pp. 415–421.




Measurements in Triaxial Tests,” Geotech. Test. J., Vol. 24, No. 2, pp. 193–199.

Bhandari, A. R., Powrie,W., and Harkness, R. M., 2012, “A Digital Image-Based Deformation

Measurement System for Triaxial Tests,” Geotech. Test. J., Vol. 35, No. 2, pp. 209–226.


Triaxial Apparatus,” Proceedings of the Fifth International Conference on Soil

Mechanics and Foundation Engineering, Vols. 1/3, Paris, July 17–22, Institution of Civil

Engineers, London, pp. 13–21.

Clayton, C. R. I., Khatrush, S. A., Bica, A. V. D., and Siddique, A., 1989, “The Use of Hall


No. 1, pp. 69–76.





pp. 98–103.

Geomagic Design X; Version 17 2015. “3D Computer-Aided Design (CAD) software,” 3D

Systems, Rock Hill, SC.


No. 3, pp. 187–201.



Leong, E. C., Agus, S. S., and Rahardjo, H., 2004, “Volume Change Measurement of Soil

Specimen in Triaxial Test,” Geotech. Test. J., Vol. 27, No. 1, pp. 47–56.



pp. 324–339.

71



pp. 103–109.



Ng, C. W. W., Zhan, L. T., and Cui, Y. J., 2002, “A New Simple System for Measuring Volume

Changes in Unsaturated Soils,” Can. Geotech. J., Vol. 39, No. 3, pp. 757–764.

Nübel, K. and Weitbrecht, V., 2002, “Visualization of Localization in Grain Skeletons With

Particle Image Velocimetry,” J. Testing Eval., Vol. 30, No. 4, pp. 322–329.






Eng. Geol., Vol. 85, No. 3, pp. 239–250.

PhotoModeler Scanner; Version 2015.0.0, 2015, “3D Measurements and Models Software,”

Eos Systems, New York.

Puppala, A. J., Katha, B., and Hoyos, L. R., 2004, “Volumetric Shrinkage Strain Measurements

in Expansive Soils Using Digital Imaging Technology,” Geotech. Test. J., Vol. 27,

No. 6, pp. 547–556.




With Spatially Varying Parameters,” J. Geotech. Geoenviron. Eng., Vol. 133, No. 12,

pp. 1567–1576.


Using Digital Image Analysis (DIA) Technique,” Soils Found., Vol. 47, No. 1,

pp. 67–78.

Salazar, S. E. and Coffman, R. A., 2014, “Design and Fabrication of End Platens for Acquisition

of Small-Strain Piezoelectric Measurements during Large-Strain Triaxial Extension and

Triaxial Compression Testing,” Geotech. Test. J., Vol. 37, No. 6, pp. 948–958.

doi:10.1520/GTJ20140057.

72

Salazar, S. E. and Coffman, R. A., 2015, “Consideration of Internal Board Camera Optics for

Triaxial Testing Applications,” Geotech. Test. J., Vol. 38, No. 1, pp. 40–49.

doi:10.1520/GTJ20140163.






Testing,” Acta Geotech., Vol. 10, No. 1, pp. 55–82.

73

CHAPTER 5: DISCUSSION OF "A PHOTOGRAMMETRY-BASED METHOD TO

MEASURE TOTAL AND LOCAL VOLUME CHANGES OF UNSATURATED SOILS

DURING TRIAXIAL TESTING" BY ZHANG ET AL., 2015


The Zhang et al. (2015) publication was discussed in this chapter. The Zhang et al. (2015)

manuscript contained a description of a photogrammetric method for determining total and local

volume changes of soil specimens during triaxial testing. Like the other camera-based triaxial

monitoring techniques found in the literature, Zhang et al. (2015) used cameras external to the

testing cell and therefore had to account for refraction effects and limited visibility of test

specimens through the cell wall. Despite this difference, the manuscript caught the attention of

the author, because of the similarities in the photogrammetric processing of results. This

manuscript echoes the Zhang et al. (2015) discussion of the limitations of non-photogrammetric

methods for determining triaxial specimen volume, describes the limitations of the Zhang et al.

(2015) work, and offers comparison with the methodology presented in Salazar and Coffman

(2015) and Salazar et al. (2015).

The full citation for this manuscript (Salazar and Coffman 2015) is included in Section

5.2. The discussion is presented in Section 5.3, which includes discourse on the apparent

improper triaxial testing techniques of the Zhang et al. (2015) publication (Section 5.3.1), a

discussion of the cell wall deformation corrections and least-square optimization (Section 5.3.2),

and photogrammetric methods (Section 5.3.3).

5.2. Discussion of "A Photogrammetry-based Method to Measure Total and Local Volume

Changes of Unsaturated Soils During Triaxial Testing" by Zhang et al., 2015

Reference

Salazar, S. E. and Coffman, R. A., “Discussion of ‘A Photogrammetry-based Method to Measure

Total and Local Volume Changes of Unsaturated Soils During Triaxial Testing’ by Zhang et al.”

Acta Geotechnica, Vol. 10, No. 5, pp. 693-696. doi:10.1007/s11440-015-0380-1.

74

5.3. Discussion

Zhang et al. (2015), in the paper entitled ‘‘a photogrammetry-based method to measure

total and local volume changes of unsaturated soils during triaxial testing,’’ presented a method

for measuring the volume and strain of saturated and unsaturated soil specimens during triaxial

tests. Specifically, the presented method utilized a single, external digital camera, to capture

images of a triaxial testing apparatus and of the corresponding soil specimen within the cell.

Photogrammetric analyses were performed using commercially available photogrammetry

software. Utilizing the Zhang et al. (2015) modeling technique, ringed automatically detected

(RAD) coded targets were utilized to locate common points within each of the captured images,

and then, photogrammetry techniques were employed to assign physical, three-dimensional,

coordinates to each of the points.

A comprehensive and categorized review of triaxial volume measurement methods that

were found in the literature was presented in the Zhang et al. (2015) article. The methods that

have been previously utilized to measure the volume of saturated and unsaturated soil specimens,

during triaxial testing, were presented in a clear and concise manner by citing advantages and

disadvantages, accuracy, and costs associated with each method (Table 1 within Zhang et al.

(2015)). Furthermore, the current state of the art of photograph-based measurements was

explained. As stated in Zhang et al. (2015), the validity of other photograph-based volume

measurements [digital image analysis (DIA), digital image correlation (DIC), and particle image

velocimetry (PIV)] suffer from unrealistic, fundamental assumptions and limitations.

Specifically, the DIA methods require accurate and precise control of the relative camera

location and of the camera orientation relative to the triaxial cell soil specimen. The DIC and

PIV methods typically cannot provide total volume measurements; however, Bhandari et al.

75

(2012) utilized the DIC method and overcame some of the difficulties associated with DIC

methods to provide viable results. However, the need for true photogrammetry to accurately

measure local and global volumes of saturated and unsaturated soil specimens was presented by

Zhang et al. (2015). Moreover, each of the steps of the photogrammetric process was thoroughly

explained. The methods presented in Zhang et al. (2015) are a valuable contribution to the

literature because the methods may be used to: measure total volume, measure local volume

changes (Figure 19 within Zhang et al. (2015)), and illustrate strain localization and shear

banding within soil specimens during triaxial testing. However, Zhang et al. (2015) do not

expound upon the limitations of the presented method. These limitations include the use of: (1)

improper triaxial testing procedures and (2) photogrammetric cell wall deformation

measurements combined with least-square optimization to obtain corrected ray path

measurements.

5.3.1. Improper Triaxial Testing Techniques

An internal load cell should be utilized in triaxial testing to prevent the need for piston

uplift and piston friction corrections. Silicone oil, instead of water, is commonly used within the

cell, as the cell fluid, when an internal load cell is utilized. The index of refraction for silicone oil

differs from the index of refraction for water, which may affect the observed results in a similar

manner to that shown for difference in the indices of refraction for air and water that is presented

in Figure 1 of the Zhang et al. (2015) article. Furthermore, because of the use of an external

camera, the cleanliness of the acrylic cell wall (which can be compromised within a soil

mechanics laboratory) may also affect the results.

Although Zhang et al. (2015) utilized an impressive back pressure saturation technique in

which the sand was infused with CO2 and then subjected to 400 kPa of back pressure to obtain a

76

B value of 0.98, the back pressure saturation technique was for naught because the cell pressure

was reduced from 435 to 100 kPa and the back pressure was reduced from 100 to 0 kPa prior to

shearing. The reduction in cell pressure and back pressure most likely resulted in effervescence

of the pore fluid and therefore desaturation of the sand specimen to an unknown state of suction

within the soil specimen. Thereby, even though higher cell pressures (600 kPa) were utilized to

determine the accuracy of the method, these pressures were not utilized for the triaxial testing of

the soil specimens. This brings into question whether the Zhang et al. (2015) method will work if

the cell is pressurized under high cell pressures that are commonly required to back pressure

saturate and overconsolidate clay specimens (1035 kPa).

5.3.2. Utilization of Cell Wall Deformation Combined with Least-Square Optimization

The Zhang et al. (2015) method utilized images that were captured from outside of the

cell. Therefore, ray tracing was required to correct for the refraction effects of the light (1) at the

confining fluid–cell wall interface and (2) at the cell wall–air interface. Additionally, the method

considered deflection of the cell wall during pressurized tests by including RAD-coded targets

that were adhered to the outer surface of the cell wall and to the load frame (considered fixed

control points for reference purposes). It was assumed that the cell wall deformed in a uniform,

radial pattern. Furthermore, deformation of the cell wall was not considered above 600 kPa, even

though typical triaxial tests may reach confining fluid pressures above 1000 kPa. It is suggested

that the correction for cell wall flexure be characterized for a full range of pressures that are

commonly achieved during a typical triaxial test (up to 1035 kPa for acrylic cell walls).

Furthermore, it may be a useful contribution to show a sensitivity study of the photogrammetric

method as applied to multiple optical media.

77

In Section 2.1.1, Zhang et al. (2015) identified the problems associated with the

utilization of the measurement of the cell fluid for determining the volume change of a triaxial

specimen. However, Zhang et al. (2015) utilized a similar method, albeit in the form of a

photogrammetric correction instead of a calibration procedure, to account for the change in the

ray path that is associated with the cell wall deformation during pressurization/depressurization

of the cell wall deformation under a constant applied pressure (creep). Moreover, the camera that

was utilized was a lensed camera. Before analysis of captured images, photogrammetric software

was used by Zhang et al. (2015) to correct for lens distortions (thereby modeling the lensed

camera as a pinhole camera).

Recently, as presented in Salazar and Coffman (2015a, 2015b), a triaxial insert board

camera pinhole aperture (BCPA) camera system was developed by researchers at the University

of Arkansas. Although utilization of eight cameras was presented in the Salazar and Coffman

(2015a) article, the system was further modified to consist of ten small cameras (five cameras per

tower, with the two towers being diametrically opposed), as presented in Salazar and Coffman

(2015b). Two towers were required because the drainage lines for the top platen prevented a full

360º rotation of only one tower. Therefore, using the BPCA tower system, ten photographs were

acquired at a given position, while each of the towers completed a 155º rotation around the

specimen. The BCPA system was fully submerged in the silicone confining fluid, and the BCPA

was capable of being saturated and pressurized under pressures of up to 1035 kPa. Therefore, the

BCPA system enabled testing conditions that were similar to those that are commonly used

instead of requiring that the cell pressure and back pressure be reduced prior to shearing. The use

of the BPCA camera system: (1) reduces the complicated geometry of the camera location and

orientation by utilizing photogrammetry to derive the exact camera location and orientation, (2)

78

does not require determination of the best fit of the shape and location of the acrylic cell, (3)

does not require ray tracing or Snell’s law because the photographs are acquired from within the

cell fluid, and (4) provides an alternative to externally acquired photogrammetric methods.

5.3.3. Testing Procedures and Photogrammetric Methods

Zhang et al. (2015) performed isotropic compression tests for a stainless steel specimen

to measure the accuracy for the photogrammetry method. Tests were performed on a 5.08 cm

diameter by 10.16 cm tall stainless steel specimen that was tested within a 10.16 cm diameter by

20.32 cm tall acrylic cell with a 0.61 cm thick cell wall that had a refractive index of 1.491.

Approximately 50 photographs were acquired for each testing condition (0 kPa in air without cell

wall; 0, 200, 400, 600 kPa in water), by taking at least five photographs from different

orientations for each area/point of interest to ensure ‘‘sufficient overlap between adjacent

pictures.’’ Targets numbering 16, 218, and 336 were utilized to identify the load frame, acrylic

cell, and stainless steel specimen, respectively.

Drained triaxial tests were also performed on a saturated sand specimen to determine the

total and local volume measurements of the specimen during the triaxial tests. Unlike the triaxial

cell that was utilized for the isotropic compression tests on the stainless steel cylinder, a larger

triaxial cell with larger specimens and fewer targets was used for the triaxial tests conducted on

the saturated sand specimens. Specifically, a 7.1 cm by 13.7 cm specimen was tested within a

16.51 cm diameter by 30.48 cm tall triaxial cell that had a cell wall thickness of 0.97 cm and a

refractive index of 1.491. Also, 174 and 176 targets were utilized to identify the acrylic cell and

sand specimen, respectively, within the 25 photographs that were acquired for each testing

condition (at every 2–3 mm of vertical displacement…until a total displacement of 15 mm is

reached). The reason for using 336 targets adhered to the specimen was never explained, nor

79

justified. Furthermore, it was not clear how point capture redundancy eliminates any assumptions

regarding the specimen deformations. This statement requires further explanation. A parametric

study of the accuracy achieved, for different numbers of points utilized, would be a useful

contribution to the literature and would help other researchers make decisions on the level of

refinement required to achieve a desired level of accuracy. Also, a parametric study would aid in

determining the minimum number of targets required to measure the total and local volumes of

specimens. Although the results presented by Zhang et al. (2015) would indicate that the method

is capable of achieving high accuracy (<0.25 % error), the method is computationally intensive,

due to the effects of refraction and cell wall deformation.

At the University of Arkansas, researchers performed tests on a brass specimen with

nominal dimensions of 3.8 cm in diameter and 7.6 cm in height that contained 273 targets;

thereby, the University of Arkansas specimen was smaller than the specimen used by Zhang et

al. (2015) and contained more targets on the surface of the soil specimen. Each of the drainage

lines prevented direct viewing of 25º of the specimen; however, the photos collected near the

drainage lines allowed for points within these locations to be viewed in at least six photos,

instead of the customary ten photos that were used for the other points. In addition to the tests on

a brass specimen, at various times during triaxial tests on soil specimens [prior to confinement,

during back pressure saturation, prior to consolidation, during consolidation, after consolidation,

and during shearing (1, 3, 6, 9, 12, and 15 % axial strain)], photographs were obtained by

rotating the towers at a desired increment ranging from a minimum of 45º increments to a

maximum of 5º increments. Specifically, ranging from a minimum of 40 pictures per observation

(10 pictures per increment, and 4 increments) to a maximum of 320 pictures per observation (10

pictures per increment, and 32 increments), respectively.

80

The same procedures that were utilized by Zhang et al. (2015) for the image analysis in

air are common accuracy prediction methods, and these procedures were also utilized by Salazar

and Coffman (2015b). However, the Salazar and Coffman (2015b) method offered a viable

alternative to the Zhang et al. (2015) method, by placing photogrammetric equipment within the

triaxial cell instead of outside of the triaxial cell. The lensless camera equipment that was

devised by Salazar and Coffman (2015a) allowed for direct, unobstructed observation of a

specimen during testing. Therefore, computationally intensive corrections to account for the

effects of refraction through multiple types of media and deformation of the cell wall were

eliminated. In a similar fashion to the Zhang et al. (2015) method, the Salazar and Coffman

(2015b) method utilized the same principles of photogrammetry (using PhotoModeler Scanner

software (Eos Systems, Inc. (2015)) and RAD-coded targets to create a point cloud of the

specimen surface. In the Salazar and Coffman (2015b) method, the point cloud was then meshed

to obtain an accurate, three-dimensional reconstruction of the specimen, whereupon the mesh

was imported into Geomagic Design software (3D Systems, Inc., 2015) to calculate the volume

of the specimen. The volumetric strain was then obtained by subtracting the volume of the

specimen at various times from the initial volume and then dividing by the initial volume.

Whereas Zhang et al. (2015) utilized a proprietary program (PhotoSoilVolume) to handle the

cumbersome optical correction process through to volume calculation, the Salazar and Coffman

(2015b) method required only commercially available software to calculate total specimen

volumes. As described in Salazar and Coffman (2015a), the optical components of internal

photogrammetric instrumentation were designed, fabricated, and tested for triaxial testing

applications to overcome the aforementioned drawbacks of external methods. The cameras were

81

also designed to overcome the challenges of internal instrumentation (space, confining fluid,

focal length, cell pressure, and specimen coverage).

In summary, the contribution produced by Zhang et al. (2015) is significant and provides

an advancement of the state of knowledge of external photograph-based measurements of triaxial

specimens. However, the use of internal cameras like those presented in Salazar and Coffman

(2015a, 2015b), instead of an external camera, is suggested to further advance the

photogrammetric technique. Specifically, the use of internal cameras will facilitate a reduction in

computational demands by (1) eliminating the need for a cell deformation/position correction

and by (2) eliminating the need for ray tracing and least-square optimization. Although the

Salazar and Coffman (2015b) method is less computationally costly than the method presented

by Zhang et al. (2015), the cost and reproducibility of required photogrammetric equipment are

approximately equivalent. Therefore, it appears that the Salazar and Coffman (2015a) method is

a viable alternative method for acquiring total and local volume changes of soil specimens during

triaxial testing.

82

5.4. References

3D Systems, Inc., 2015, Geomagic Design X (Version 17). 3D Computer-Aided Design

(CAD) Software. http://www.geomagic.com/en/products/design/overview



Eos Systems, Inc., 2015, PhotoModeler Scanner (Version 2015.0.0). 3D Measurements and

Models Software. http://www.photomodeler.com/products/scanner/default.html

Salazar, S. E., Barnes, A., and Coffman, R. A., 2015b, “Development of an Internal Camera


No. 4, pp. 549-555. doi:10.1520/GTJ20140249.



doi:10.1520/GTJ20140163.



Testing,” Acta Geotech., Vol. 10, No. 1, pp. 55-82. doi:10.1007/s11440-014-0346-8.

83

CHAPTER 6: CLOSURE TO "DISCUSSION OF 'DEVELOPMENT OF AN

INTERNAL CAMERA-BASED VOLUME DETERMINATION SYSTEM FOR

TRIAXIAL TESTING' BY S. E. SALAZAR, A. BARNES, AND R. A. COFFMAN"

BY MEHDIZADEH ET AL., 2016


A closure to the Mehdizadeh et al. (2016) discussion paper is provided in this chapter.

The closure addresses queries that were raised by the discussion paper and clarifies the apparent

ambiguities of the previously described Salazar et al. (2015) technique. The manuscript also

provides additional testing data that shed light on the effect of pausing a triaxial test for short

periods of time (at desired axial strain intervals) to capture photographs of the surface of the

specimen. The full citation for this manuscript (Salazar et al. 2017) is included in Section 6.2 and

the body of the closure is presented in Sections 6.3 and 6.4.

6.2. Closure to “Discussion of ‘Development of an Internal Camera-Based Volume

Determination System for Triaxial Testing’ by S.E. Salazar, A. Barnes, and R.A. Coffman”

by Mehdizadeh et al., 2016

Reference

Salazar, S. E., Barnes, A., and Coffman, R. A., “Closure to “Discussion of ‘Development of an

Internal Camera-Based Volume Determination System for Triaxial Testing’ by S. E. Salazar, A.

Barnes, and R. A. Coffman” by A. Mehdizadeh, M. M. Disfani, R. Evans, A. Arulrajah, and D. E.

L. Ong,” Geotechnical Testing Journal, Vol. 40, No. 1, 2017, pp. 47-51.

doi:10.1520/GTJ20160154.

6.3. Abstract

The discussion paper, written by Mehdizadeh et al., provided discourse on a

technical note entitled “Development of an Internal Camera-Based Volume Determination

System for Triaxial Testing,” which presented a novel technique of photographically

monitoring soil specimens during triaxial tests by utilizing small board cameras internal to

the triaxial cell. Here, a closure to the discussion paper was provided; queries raised by the

84

discussers were addressed, ambiguities were clarified, and additional testing data to support

the closure were provided.

Keywords: triaxial testing, photogrammetry, volume measurement, local deformation

6.4. Introduction

The authors appreciate Mehdizadeh et al. (2016), herein after referred to as the

discussers, for their interest in the technical note entitled “Development of an Internal

Camera-Based Volume Determination System for Triaxial Testing.” The authors believe

that the discussers (1) primarily wished to highlight the ambiguities contained within the

technical note, while also pointing to the work of Uchaipichat et al. (2011), and (2) offered a

simple solution to deal with optical distortion corrections. In this closure, the authors

addressed the comments put forth by the discussers, in the order in which they appeared in

the discussion paper, to clarify the ambiguities within the original technical note.

The discussers mentioned that Uchaipichat et al. (2011) monitored the volumetric

strain of a soil specimen during a triaxial compression test with the aid of only two cameras

(external to the confining cell). However, the authors agree with Uchaipichat et al. (2011)

that the digital image analysis method that was employed by Uchaipichat et al. (2011)

cannot be used to reliably determine the specimen volume in the case of nonuniform

deformation. The volume cannot be accurately measured using this technique because the

camera setup does not capture localized strain (such as observed in shear banding) and relies

heavily on averaging around the circumference of the specimen. While the Uchaipichat et al.

(2011) method may be accurate enough for some applications (such as determining the total

volumetric strain or approximating the radial deformation at mid-height), the technique may

not be suitable for applications where it is desired to determine absolute sample volume or

85

to characterize the development of local deformations (by tracking individual targets on the

specimen surface). Although Uchaipichat et al. (2011) showed that the averaging technique

correlated well with the burette measurements for the test presented in the manuscript, the

use of only one frontal view image and one side view image cannot do justice in every case,

especially in the case of non-uniform deformation.

The discussers’ demonstration that the need to account for the “distortion of light,

cell curvature, and camera lens” could be eliminated altogether by basing all relative

measurements on a point of reference is intriguing. The authors commend Uchaipichat et al.

(2011) and the discussers for avoiding cumbersome corrections for optical distortions;

however, this simple calibration procedure can only be used to determine changes in total

specimen volume relative to an a priori volume. It is not clear how the initial volume of the

specimen would be obtained with sufficient accuracy to allow for any absolute

measurements before, during, or after the test. Any initial volume measurements, however

meticulous, would be for naught once the specimen was placed inside of the cell and set up

for testing (i.e., piston contact with specimen, filling of the cell with confining fluid).

Furthermore, it is not clear how the discussers suggest to correct for cell wall deformation

during tests when the confining pressure in the cell changes throughout the stages of testing

(during back pressure saturation, consolidation, and shearing). As listed in Table 1 in

Salazar and Coffman (2014), there are four stress paths where the cell pressure changes

during the shearing stage. Moreover, Zhang et al. (2015a) and Salazar and Coffman (2015b)

documented that the amount of cell wall deformation might be a significant factor when

tracing rays through the media surrounding the specimen (confining fluid, cell wall, air).

86

The discussers noted correctly that due to the limited field of view for each of the

board camera devices that were presented in Salazar et al. (2015), the size of the observed

specimens was limited to nominal dimensions of 38.1-mm in diameter and 76.2-mm in

height. The triaxial stress path testing performed at the University of Arkansas is primarily

for stress-strain behavior to derive parameters required for constitutive modeling. The

specimens that are typically tested are primarily soft soils that have been (1) trimmed from a

Shelby tube sample, or (2) reconstituted in one of the 38.1-mm diameter, static weight slurry

consolidometers (in a similar fashion to Zhao and Coffman (2016) and Zhao et al. (2016))

prior to K0 reconsolidation within the triaxial cell. Furthermore, this smaller specimen size is

favored because it allows for reduced consolidation time over larger specimen sizes. It

should alleviate the discussers’ concern to know that the internal photogrammetry system

could easily be adapted to larger cells and testing of larger specimens. In fact, a larger cell

would allow for more space between the specimen and camera tower, increasing the vertical

and horizontal area viewed by each camera. This could also serve to reduce the number of

internal board cameras required, thereby reducing the number of images captured and the

amount of photogrammetric processing required.

The system presented in Salazar and Coffman (2015a, 2015b) and Salazar et al.

(2015) is neither overly complicated nor costly (especially as compared to a DSLR camera

and lens). However, it does require knowledge of photogrammetry for implementation. The

term “photogrammetry” was misused throughout the discussion by Mehdizadeh et al.

(2016); the term “photogrammetry” was interchanged with other photographic methods

(including digital image analysis and digital image correlation). Salazar and Coffman

(2015a, 2015b), Salazar et al. (2015), as well as Zhang et al. (2015a, 2015b), have proposed

87

that the application of photogrammetry (or more accurately, stereophotogrammetry) is more

robust than other digital imaging techniques for determining the total- and local- radial,

axial, and volumetric strains. Specifically, photogrammetry overcomes the weaknesses of

other photographic methods while becoming increasingly easier to apply with the increasing

availability of various commercial and open-source photogrammetry processing software

packages. In addition, other photogrammetric methods, including open-source structure

from motion (SfM) and multi-view stereo (MVS) applications, using more recently

developed computer vision techniques, merit further investigation. Unlike the

stereophotogrammetry technique that was discussed in Salazar et al. (2015,2016), no prior

camera calibrations would be required using the MVS technique. Therefore, overall

processing times (even for the relatively large number of images captured with the internal

camera based system) would be dramatically reduced, and the reconstructed 3D model

would contain more surface detail (Furukawa and Hernández 2013).

The discussers also mentioned that the use of silicone oil for the confining fluid, in

place of water, would necessitate the use of specialized flow pumps that are not commonly

available. In fact, the adaptation of silicone oil as confining fluid has become commonplace

in research laboratories that utilize internal load cells, and there are several triaxial apparatus

manufacturers that sell flow pumps for this very purpose. As an aside, the internal load cells

are necessary in advanced triaxial stress path testing programs to account for the effects of

piston uplift and piston friction (Race and Coffman 2011, Salazar and Coffman 2015b). The

authors agree with the discussers that the choice of confining fluid has no particular impact

on external photography of the triaxial specimen (as long as the fluid is not opaque and the

index of refraction is taken into account). It was previously highlighted that the adaptation

88

of open-body internal camera equipment was made possible by the already in-place practice

of using inert silicone oil as a confining fluid. The oil allows the camera devices and

associated electronics to be fully saturated and fully submerged in the confining fluid

without becoming damaged. Furthermore, the open-body style of the board cameras has

been proven to eliminate any pressure differentials by allowing the fluid to fill the lensless

cameras, including behind the pinhole aperture (as explained in Salazar and Coffman

2015a). This open body is a key design element of the camera devices, as it would be

impractical (and perhaps even impossible) to design compact, waterproof camera housings

capable of withstanding the pressures that are present within the confining cell during a

typical triaxial test. Furthermore, due to the lack of difference in indices of refraction

between the lens and the fluid, the authors’ discussion of confining fluid, as related to

refraction, was only provided to highlight the fact that the use of a lens submerged within

the fluid does not function as intended. Specifically, the index of refraction of a typical lens

is around 1.5 (depending on the material), which is too close to the index of refraction of

water (around 1.33) or silicone oil (1.397, as tested). The refraction of light through a lens in

air requires a larger difference (i.e. the index of refraction of air is approximately 1.0).

Therefore, the use of a lensless design was necessary to function within the cell; the

elimination of typical distortions associated with lenses was a fortuitous side-effect,

resulting in less corrections during photogrammetric calibration and processing. The use of a

lensless camera design is not without problems, due to the necessity of having good lighting

to allow the camera sensors to collect data and to reduce vignetting at the edges of the

image. However, proper lighting is still a key factor in collecting quality data when using

external DSLR photography.

89

The authors commend the discussers for their approach to demonstrating a simple

and practical method of monitoring a triaxial specimen from the exterior of the cell, by

following the Uchaipichat et al. (2011) method. Particularly, the authors appreciate the

discussers’ use of stainless steel calibration specimens with known dimensions for

reference, as this practice is currently missing from the available body of literature for

photographic observation of triaxial specimens. In a similar fashion, the authors have

performed multiple comparison tests using brass and acrylic specimens with known

dimensions to validate the internal photogrammetry technique. The results of these tests

were documented in Salazar et al. (2016). Furthermore, the authors have continued on to

demonstrate the capabilities of the internal photogrammetry approach by monitoring soil

specimens during triaxial compression and extension tests (Salazar et al. 2016). Because no

universal comparison exists to assess the error for new volume measurement techniques

(and often there is no comparison to an external reference at all), the authors have attempted

to evaluate the difference in measured volume from a reference measurement. In Table 1 of

Salazar et al. (2016), a series of volume measurements for an acrylic specimen was

presented. The volume of the acrylic specimen was determined using a water displacement

technique (by adapting the Proctor mold volume determination method from ASTM D698-

12e2), manual measurements using a pi tape and calipers, 3D scan measurements, external

DSLR photogrammetry (camera located outside of cell, in air), and internal photogrammetry

(cameras located in cell filled with silicone oil confining fluid). The measured volume of the

acrylic specimen, determined using the internal photogrammetry approach, fell within 0.13

% difference from the reference volume. Although the reference measurement technique for

this example was the water displacement technique (because it was based on an ASTM

90

standard), the measured volumes of the acrylic specimen fell within 0.5 % of the reference

for all five volume determination techniques.

The discussers commented that the Salazar et al. (2015) technique required rotation

of the camera tower platform around the specimen to capture images of the entire surface.

To ensure that there were no changes to the specimen during the image-capturing process,

the test was paused at the desired intervals. The authors concede that the acquisition of the

necessary images may be time-consuming; however, the short pauses during a test did not

cause problems in the stress path for the test (Figures 6.1 and 6.2) and excess pore water

pressure returned to the prescribed behavior after each pause during the test (Figure 6.3).

Furthermore, an advantage of the technique is that the camera towers may be rotated to

occupy any desired rotation interval around the specimen. Therefore, the acquisition time

and subsequent processing time may be significantly reduced with a reduced number of

images (i.e., greater angles between the camera intervals).

91

Figure 6.1. Comparison of deviatoric stress as a function of mean stress for a reduced

triaxial extension test with pauses and without pauses for capturing photographs.

Figure 6.2. Comparison of deviatoric stress as a function of axial strain for a reduced

triaxial extension test with pauses and without pauses for capturing photographs.

-200

-150

-100

-50

0

50

100

150

200

0 50 100 150 200 250 300 350 400

Dev

iato

ric

Str

ess,

q =

σ1

-σ

3 ,

[kP

a]

Mean Stress, p' = (σ1' + 2σ3')/3, [kPa]

RTE Test with Pauses for Photographs

RTE Test without Pauses for Photographs

-200

-150

-100

-50

0

50

100

150

200

-12-10-8-6-4-20

Dev

iato

ric

Str

ess,

q =

σ1

-σ

3 ,

[kP

a]

Axial Strain, εa , [%]



Specimen Parameters:

wc = 50%, OCR = 1,

310 kPa K0 Consolidation


wc = 50%, OCR = 1,


92

Figure 6.3. Comparison of excess pore water pressure development as a function of axial

strain for a reduced triaxial extension test with pauses and without pauses for capturing

photographs.

It was mentioned that during the photographic reconstruction of the stainless steel

weights, the discussers experienced some difficulty establishing the specimen edges within

the cell. The advantage of the photogrammetry techniques presented in Zhang et al. (2015a)

and Salazar et al. (2015) is that the long edges (profile) of the specimen need never be

established, because photogrammetry allows for the triangulation of individual points on the

surface of the specimen in 3D space. However, similar to the discussers’ experience, the

authors have also had some difficulty in establishing reliable points on the ends (top and

bottom) of the specimen. This difficulty was overcome by manually picking common

marker points, within each photo, along the top and bottom edges of the specimen within the

photogrammetry software.

-75

-50

-25

0

25

-12-10-8-6-4-20

Ex

cess

Po

re P

ress

ure

, Δ

u,

[kP

a]

Axial Strain, εa , [%]




wc = 50%, OCR = 1,


93

As mentioned in Salazar and Coffman (2015b), the authors share the discussers’

concerns that cell wall cleanliness and obstruction due to triaxial cell apparatus (frame rods,

cell wall confining rings) are factors not to be overlooked when photographically

monitoring specimens from the exterior of the cell. However, the discussers successfully

demonstrated that the volumetric strain of a triaxial sample could be determined to a

reasonable level of accuracy without having to take into account cumbersome corrections:

(1) for optical distortions due to light refraction at the confining fluid-cell wall and cell wall-

air interfaces, and (2) due to cell wall curvature. The authors suggest that for future

applications, where only relative measurements are of interest to the discussers, more

camera positions should be utilized within the Uchaipichat et al. (2011) methodology to

capture more images of the specimen to increase the accuracy of non-uniform volumetric

strain measurements.

94

6.5. References

ASTM D698-12e2, 2012, "Standard Test Methods for Laboratory Compaction

Characteristics of Soil Using Standard Effort (12 400 ft-lbf/ft3 (600 kN-m/m3))",

ASTM International, West Conshohocken, PA, www.astm.org.

doi:10.1520/D0698-12E02.

Furukawa, Y. and Hernández, C., 2013, “Multi-View Stereo: A Tutorial,” Found. Trends

Comput. Graphics Vis., Vol. 9, Nos. 1–2, pp. 1–148.

Mehdizadeh, A., Disfani, M. M., Evans, R., Arulrajah, A., and Ong, D. E. L., 2016,

“Discussion of ‘Development of an Internal Camera-Based Volume Determination

System for Triaxial Testing’ by S. E. Salazar, A. Barnes and R. A. Coffman,”

Geotech. Test. J., Vol. 38, No. 4, 2015, pp. 549–555.

Race, M. L. and Coffman, R. A., 2011, “Effects of Piston Uplift, Piston Friction, and

Machine Deflection in Reduced Triaxial Extension Testing,” ASCE Geotechnical

Special Publication No. 211, Proceedings GeoFrontiers 2011: Advances in

Geotechnical Engineering, ASCE, Reston, VA, pp. 2649–2658.

Salazar, S. E., Barnes, A., and Coffman, R. A., 2015, “Development of an Internal Camera-

Based Volume Determination System for Triaxial Testing,” Geotech. Test. J.,

Vol. 38, No. 4, pp. 549–555.

Salazar, S. E. and Coffman, R. A., 2014, “Design and Fabrication of End Platens for

Acquisition of Small-Strain Piezoelectric Measurements During Large-Strain

Triaxial Extension and Triaxial Compression Testing,” Geotech. Test. J., Vol. 37,

No. 6, pp. 948–958. doi:10.1520/GTJ20140057.

Salazar, S. E. and Coffman, R. A., 2015a, “Consideration of Internal Board Camera Optics

for Triaxial Testing Applications,” Geotech. Test. J., Vol. 38, No. 1, pp. 40–49.

doi:10.1520/GTJ20140163

Salazar, S. E. and Coffman, R. A., 2015b, “Discussion of ‘A Photogrammetry-Based

Method to Measure Total and Local Volume Changes of Unsaturated Soils During

Triaxial Testing’ by Zhang et al.,” Acta Geotech., Vol. 10, No. 5, pp. 693–696.

Salazar, S. E., Miramontes, L. D., Barnes, A., Bernhardt, M. L., and Coffman, R. A., 2016,

“An Internal Close-Range Photogrammetry Approach to Volume Determination for

Triaxial Testing,” Acta Geotech. (under review).


Apparatus for Testing Unsaturated Soils,” Geotech. Test. J., Vol. 34, No. 5,

pp. 424–432.

95

Zhang, X., Li, L., Chen, G., and Lytton, R., 2015a, “A Photogrammetry-Based Method to


Testing,” Acta Geotech., Vol. 10, No. 1, pp. 55–82.

Zhang, X., Li, L., Chen, G., and Lytton, R., 2015b, “Reply to ‘Discussion of “A

Photogrammetry-Based Method to Measure Total and Local Volume Changes of

Unsaturated Soils During Triaxial Testing” by Zhang et al.’ by Salazar and

Coffman,” Acta Geotech., Vol. 10, No. 5, pp. 697–702.

Zhao, Y. and Coffman, R. A., 2016, “Back-Pressure Saturated Constant-Rate-of-Strain

Consolidation Device With Bender Elements: Verification of System Compliance,”

J. Test. Eval., Vol. 44, No. 6, pp. 2375–2386.

Zhao, Y., Mahmood, N. S., and Coffman, R. A., 2016, “Small-Strain and Large-Strain

Modulus Measurements With a Consolidation Device,” J. Test. Eval. (under review).

96

CHAPTER 7: VERIFICATION OF AN INTERNAL CLOSE-RANGE

PHOTOGRAMMETRY APPROACH FOR VOLUME DETERMINATION

DURING TRIAXIAL TESTING


A comprehensive description of the internal camera-based photogrammetry technique for

triaxial testing, that was developed at the University of Arkansas (Salazar and Coffman 2015a,

2015b, 2016; Salazar et al. 2015, 2017), is presented in this chapter. A series of sensitivity

studies were performed to evaluate the accuracy, precision, and feasibility of the technique.

Furthermore, the technique was implemented for two undrained triaxial tests on soil specimens.

Specifically, one conventional triaxial compression (CTC) and one reduced triaxial extension

(RTE) test were performed on slurry-consolidated, reconstituted kaolinite soil specimens. Results

from these tests, discussion of the limitations of the technique, and anticipated improvements to

the technique are presented.

The limitations of the included manuscript (Salazar et al. 2017) are discussed in


background for the manuscript are described in Sections 7.4 and 7.5. Section 7.6 presents the

evaluation of the internal photogrammetry technique. Specifically, the calibration of board

cameras, derivation of camera stations, determination of photograph intervals, capture of

photographs within confining fluid, photogrammetric reconstruction, and volume determination

are presented in Sections 7.6.1 through 7.6.6. Contained within Section 7.6.7 is a description of

the method used to determine the accuracy of the internal photogrammetry technique, which

included comparison of results from five different volume determination methods. Limitations

and sources of error are discussed in Section 7.6.8. The methods that were used for

97

implementation of the technique during triaxial compression and triaxial extension tests are

detailed in Section 7.7. Results from the sensitivity studies and from the triaxial tests are

discussed in Section 7.8. Finally, conclusions are presented in Section 7.9.


Although the manuscript contained within this chapter clarifies and further expounds on

the technique that was introduced in preceding publications, there are limitations to the work.

The various sensitivity studies that were completed as part of the evaluation of the technique

involved primarily analog (dummy) specimens. The manuscript also described the

implementation of the technique for two triaxial tests; however, these tests were undrained. It

was therefore not possible to compare changes in specimen volume, as determined using the

photogrammetry technique, with changes in pore fluid volume, as measured by the pore fluid

pump. Furthermore, the work only describes one triaxial compression and one triaxial extension

test. No repeat tests were performed to determine the precision of the technique for a given

triaxial test.

7.3. Verification of an Internal Close-Range Photogrammetry Approach for Volume

Determination During Triaxial Testing

Reference

Salazar, S. E., Miramontes, L. D., Bernhardt, M. L., and Coffman, R. A., “Verification of an

Internal Close-Range Photogrammetry Approach for Volume Determination During Triaxial

Testing,” Geotechnical Testing Journal. Submitted for Review. Manuscript Number: GTJ-2017-

0125.R2.

7.4. Abstract

Accurate strain and volume measurements are critical to phase relationships and strength

determination for saturated and unsaturated soils. In recent years, laboratory-based photographic

techniques of monitoring soil specimens have become more common. These techniques have

been used to reconstruct 3D models and to determine strain and volumetric changes of triaxial

98

specimens. A new technique that used digital photographs of the soil specimen, captured from

within a triaxial testing cell, was utilized. Photographs were processed using photogrammetric

software to reconstruct 3D models of the soil specimens at various times during the triaxial test.

By placing camera equipment within the cell, the technique eliminated the need to account for

optical distortions due to 1) refraction at the confining fluid-cell wall-atmosphere interface,

2) the curvature of the cylindrical cell wall, and 3) the pressure-induced deformation of the cell

wall.

Previously unreported results from sensitivity studies and accuracy measurements for the

internal photogrammetry approach are documented herein. Furthermore, through undrained

triaxial compression and extension tests, the viability of determining total and local strains,

volume changes, and total volume at any stage of triaxial testing was demonstrated. By

comparison with other volume-determination methods that are presented herein, including DSLR

camera photogrammetry, 3D scanning, manual measurements, and water displacement

techniques, a relative error of the internal photogrammetry technique of 0.13 percent was

assessed.

Keywords: triaxial testing, photogrammetry, volume measurements, local deformation

7.5. Introduction and Background

Researchers have employed various methods (both photograph- and non-photograph-

based) for monitoring soil specimens during triaxial tests. Specifically, these measurements have

enabled one or more of the following: 1) axial and radial dimensions and deformations with time,

2) local and/or total volume measurements, 3) volumetric strain calculations, and 4) shear band

characterization. Examples include double-wall cell systems, differential pressure transducers,

measurements of air and water volume changes (Bishop and Donald 1961, Ng et al. 2002, Leong

99

et al. 2004), displacement sensors (Scholey et al. 1995, Bésuelle and Desrues 2001), proximity

sensors (Clayton et al. 1989), laser scanners (Romero et al. 1997, Messerklinger and Springman

2007), digital image analysis (Macari et al. 1997, Sachan and Penumadu 2007), digital image

correlation (Bhandari et al. 2012), x-ray computed tomography (Desrues et al. 1996, Viggiani et

al. 2004), and photogrammetry (Kikkawa et al. 2006, Zhang et al. 2015a, Li et al. 2016). In

recent years, the popularity of photograph-based methods has surpassed non-photograph-based

methods due to their practicality, cost-effectiveness, and versatility. The limitations of the

photograph-based and non-photograph-based approaches were discussed in Salazar and Coffman

(2015a, 2015b), Salazar et al. (2015), and Salazar et al. (2017); the need for the use of

photogrammetry that relied upon internal cameras was presented.

Of the photograph-based triaxial monitoring examples in the literature (Macari et al.

1997, Alshibli and Sture 1999, Alshibli and Al-Hamdan 2001, Kikkawa et al. 2006, Gachet et al.

2007, Sachan and Penumadu 2007, Rechenmacher and Medina-Cetina 2007, Uchaipichat et al.

2011, Bhandari et al. 2012, Hormdee et al. 2014, Zhang et al. 2015a, Li et al. 2016, Salazar et al.

2017), only the techniques presented in Kikkawa et al. (2006), Zhang et al. (2015a) and Li et al.

(2016) utilized photogrammetry to obtain total and local volume changes of triaxial soil

specimens. The method presented in Zhang et al. (2015a, 2015b) and Li et al. (2016) involved

acquiring digital photographs of the specimen from outside of the cell wall. The photographs

were used to photogrammetrically reconstruct a digital, three-dimensional model. Due to the

refracted path of light between the specimen and the camera, computationally intensive

corrections were required to account for apparent distortion at the confining fluid-cell wall and

cell wall-atmosphere interfaces. This approach did appear to overcome previous limitations of

photograph-based measurement techniques, including Digital Image Analysis (DIA), Digital

100

Image Correlation (DIC), and Particle Image Velocimetry (PIV). The Zhang et al. (2015a) and Li

et al. (2016) methods clearly present several advantages of a photogrammetric approach, but the

implementation of the method introduces additional processing complexity to account for optical

refraction and cell wall flexure (Zhang et al. 2015a, 2015b, Salazar and Coffman 2015b, Li et al.

2016).

As an alternative to the aforementioned methods, that utilized externally-acquired

photographs, a photogrammetric technique that utilized photographs that were captured from

within the triaxial cell was introduced (Salazar and Coffman 2015a, 2015b, 2016; Salazar et al.

2015, 2017). As described in Salazar and Coffman (2015a, 2015b, 2016) and Salazar et al.

(2015, 2017), small board cameras with pinhole apertures were mounted to diametrically

opposed towers that were located within the triaxial cell. The cameras were designed to

withstand exposure to the confining fluid (silicone oil) and the typical high confining pressures

associated with triaxial testing (up to 1,035 kPa). Despite the relatively wide field of view of

each camera (~70 degrees), the confined space within the triaxial cell (11.43 cm [4.5 in.] inside

diameter) required a total of ten camera devices (five devices stacked vertically on each tower) to

ensure full photographic coverage of a given soil specimen. The towers were mounted on a

guided track that allowed for rotation around the soil specimen as limited by the two top cap

drainage lines. Each time a set of photographs was captured, the drainage lines functioned as a

datum for camera stations by providing a consistent starting point for rotation. With the aid of

two pairs of magnets (located on the towers and outside of the cell), the towers were manually

rotated and stopped at prescribed intervals. Ten photographs were captured at each interval.

Photogrammetry software (PhotoModeler Scanner 2015) was then utilized to reconstruct the

surface for any soil specimen at any given stage during the triaxial testing.

101

The primary advantage of the internal cell photogrammetry technique presented in

Salazar and Coffman (2015b, 2016) and Salazar et al. (2015, 2017) was direct observation of the

soil specimen during testing. The necessity to account for the refraction of light at the confining

fluid-cell wall and cell wall-atmosphere interfaces, as well as the curvature or deformation of the

cell wall, was therefore eliminated. Discussion of the method presented in Salazar et al. (2015)

was offered in Mehdizadeh et al. (2016), where it was claimed that yet another, simpler method

(Uchaipichat et al. 2011) could be employed to eliminate some of the cumbersome refraction

corrections. A closure to this discussion was provided in Salazar et al. (2017).

A comprehensive description of the steps used in the internal cell photogrammetry

approach is included herein. Furthermore, an evaluation of the accuracy of the approach, is

described. Three soil analog specimens were utilized for the evaluation. Specifically, an acrylic

specimen was used to verify the accuracy of the photogrammetric procedures. Additionally, a

brass specimen and a second acrylic specimen were used to examine the effect of the number of

photographs (ranging from 40 to 320 photographs) on the photogrammetric derivation of the

camera stations and on the determination of specimen volume. Undrained triaxial compression

and extension tests on kaolinite soil specimens are also described. The tests were performed to

demonstrate the viability of the internal photogrammetry approach to quantify total and local

deformations on the surface of the soil specimens during testing.

7.6. Evaluation of the Internal Photogrammetry Technique

As discussed herein, the performance of the internal cell photogrammetry approach that

was described in Salazar and Coffman (2015b, 2016) and Salazar et al. (2015, 2017) was

demonstrated by conducting a series of tests using soil analog specimens (brass and acrylic

specimens). Each step of the approach was evaluated prior to undrained triaxial compression and

102

extension testing. These steps included the 1) calibration of each of the individual board cameras,

2) derivation of camera locations and orientations, 3) determination of optimal degree of rotation

between photograph-capturing intervals, 4) capture of photographs of the acrylic analog

specimen, 5) photogrammetric reconstruction of the acrylic analog specimen, 6) determination of

the volume of the acrylic analog specimen, and 7) evaluation of the accuracy of the volume

determination method. To illustrate the full evaluation process, a flow chart is presented (Figure

7.1). As a subset of Figure 7.1, the photogrammetric processes are further described in Figure

7.2.

Where DSLR is digital single lens reflex (camera), CTC is conventional triaxial compression, RTE

is reduced triaxial extension, V is volume, ΔV is change in volume, h is height, Δh is change in

height, d is diameter, Δd is change in diameter, εa is axial strain, εv is volumetric strain, and Af is

the area of the actual failure plane.

Figure 7.1. The process used to evaluate the internal cell photogrammetry technique and to

obtain test parameters.

See Table 7.2 See Tables 7.4, 7.5 See Figs. 7.8, 7.9

Volu

mes C

alc

ula

ted

3-D Scan

DSLR Camera Photogrammetry

Manual Measurements

Water Displacement

Comparison of Volumes

CTC and RTE Testing

of Soil Specimens

Capture photos of specimen with camera towers at 20° rotation interval

for any given stage of testing



Create 3-D volumes of specimen for any given stage of testing

Calculate specimen

V, ΔV, h, Δh, d, Δd, εa, εv, Af Visualize strains

Internal Cell Photogrammetry Evaluation

See Fig. 7.2 Volume Determination

Method Comparison

Internal Cell Photogrammetry

103

Key

S1: Analog specimen (38.1 mm [1.5 in.] diameter by 76.2 mm [3.0 in.] length, nominal) with

targets used to derive location and orientation of internal cell cameras. Point cloud of targets was

fixed (as obtained from DSLR camera). Camera locations/orientations were fixed (as obtained

from the camera location/orientation step). S2: Larger analog specimen (44.5 mm [1.75 in.]

diameter by 88.9 mm [3.5 in.] length, nominal) with targets used to calculate locations of targets

on the specimen. Nomenclature: f is the focal length; w:h are the format size dimensions (width to

height ratio); x:y are the principal point coordinates; and K1, K2, K3, P1, P2 are dimensionless

distortion coefficients.

Figure 7.2. The process used to determine the volume of a specimen using internal cell

photogrammetry and to evaluate the sensitivity of photograph interval on the volume of the

specimen.



Target Identification

Capture photos of

coded calibration sheet

Create individual cell camera models

Outputs: f, w:h, x:y, K1, K2, K3, P1, P2

Create DSLR camera model

Outputs: f, w:h, x:y, K1, K2, K3, P1, P2

45° 30° 15° 5°

Capture photographs of S1 with camera towers at desired rotation interval

Capture photographs of S1 with DSLR camera

45° 30° 15° 5°

Derive camera locations and orientations

Create point cloud of coded targets located

on S1

Measure coded targets Output: physical

dimension with units

Identify/assign coded targets

Replace S1 photosets with corresponding

S2 photosets

Capture photos of S2 with camera

towers at desired rotation interval

Create point clouds of targets

located on S2

Identify/assign coded targets

Identify/assign coded target numbers on S2

Create 3-D volumes of S2

Capture photos of

coded calibration sheet

Compare volumes obtained from

45°,30°,15°, and 5° rotation intervals

See Table 7.3

Caliper

104

7.6.1. Calibration of Board Cameras

Off-the-shelf software can be used to determine the intrinsic camera and lens parameters

that describe the interior orientation of a given camera. This camera calibration process is an

important step of the photogrammetric process when a high level of accuracy is desired. All

cameras involved with the processes described below, even the lensless board cameras as

originally described in Salazar and Coffman (2015a), were fully calibrated utilizing the single-

sheet calibration procedure, as outlined by Eos Systems, Inc. (PhotoModeler Scanner 2015).

Through this method, each of the ten cameras were positioned to capture convergent photographs

of a calibration grid from multiple camera stations and orientations (±90 degree roll angles),

with calibration targets well distributed throughout the photographs. These photographs were

then processed using the photogrammetric software, resulting in a calibration data file for each

camera. The data files contained intrinsic camera parameters that included the focal length (f),

the sensor format size (w:h), the principal point (x:y), and the dimensionless distortion

coefficients (K1, K2, K3, P1, P2), as reported in Table 7.1. The intrinsic camera parameters were

imported into all future photogrammetry projects that used the board camera-acquired

photographs.

105

Table 7.1. Comparison of intrinsic camera parameters from calibration for all ten board

cameras utilized for internal photogrammetry.

Calibration Parameter

Camera Tower 1

Camera 1 Camera 2 Camera 3 Camera 4 Camera 5

Focal Length [mm] 3.3574 3.6599 3.3390 3.5936 3.5928

Format Size [mm] w: 5.145, h: 4.800 w: 5.149, h: 4.800 w: 5.150, h: 4.800 w: 5.152, h: 4.800 w: 5.148, h: 4.800

Princip. Point [mm] x: 2.573, y: 2.337 x: 2.659, y: 2.419 x: 2.427, y: 2.176 x: 2.806, y: 2.459 x: 2.782, y: 2.338

K1 3.87E-03 3.62E-03 2.37E-03 1.96E-03 2.32E-03

K2 -5.18E-05 -2.37E-04 3.89E-05 -7.22E-06 -4.96E-05

K3 0 0 0 0 0

P1 -1.96E-04 2.35E-04 1.36E-04 2.59E-04 1.72E-04

P2 2.50E-04 2.43E-04 -1.33E-04 4.49E-04 2.84E-04

Calibration Parameter

Camera Tower 2

Camera 1 Camera 2 Camera 3 Camera 4 Camera 5

Focal Length [mm] 3.4274 3.4498 3.2350 3.3464 3.5830

Format Size [mm] w: 5.147, h: 4.800 w: 5.150, h: 4.800 w: 5.153, h: 4.800 w: 5.154, h: 4.800 w: 5.150, h: 4.800

Princip. Point [mm] x: 2.823, y: 2.339 x: 2.608, y: 2.309 x: 2.423, y: 2.276 x: 2.397, y: 2.359 x: 2.370, y: 2.581

K1 4.27E-03 2.19E-03 2.75E-03 8.64E-04 2.03E-03

K2 -1.76E-04 -8.17E-05 -2.76E-05 -8.69E-05 2.05E-05

K3 0 0 0 0 0

P1 2.52E-04 1.14E-04 1.03E-04 9.82E-04 1.88E-05

P2 8.78E-05 3.78E-06 6.62E-05 -3.68E-04 -4.86E-05

Note: K1, K2, K3, P1, and P2 are dimensionless distortion coefficients.

7.6.2. Derivation of Camera Stations within the Triaxial Cell

With any photogrammetric project, it is necessary to obtain the exterior orientation

parameters (i.e. position and orientation) for each camera station used for capturing a

photograph. To derive this information for the board cameras that were internal to the triaxial

cell, the following procedure was performed. A cylindrical, brass analog specimen (38.1 mm [1.5

in.] diameter by 76.2 mm [3.0 in.] length, nominal) was wrapped with a sequence of black ringed

automatically detected (RAD) coded targets that were printed onto a sheet of white paper (to

provide contrast). The brass specimen was then placed upright on a flat surface. Additional RAD

targets were placed on the flat surface adjacent to the specimen to provide additional tie points

and improve the overall geometry and accuracy of the model. A fully calibrated, digital single

lens reflex (DSLR) camera with a fixed 28 mm lens were used to capture overlapping

106

photographs from various positions around the brass specimen (approximately 40 photographs

total). A selection of these photographs were processed using the photogrammetric software,

which automatically identified and measured each RAD target. Several measurements acquired

using a caliper (between two distant targets) were input into the software program to define the

scale. Three-dimensional coordinates for all 286 RAD target locations were then exported as a

comma-delimited text file and used as control points in subsequent projects.

The same targeted brass specimen, which was used with the DSLR camera, was then

placed within the instrumented triaxial cell and a set of photographs was captured by the internal

board cameras at five-degree intervals. Although two 20-degree sections (40 of the total 360

degrees) were left with no directly perpendicular photographs, due to the presence of the two

diametrically opposed drain lines, the entire specimen surface was observed with the internal

board cameras. The set of five-degree interval photographs (total of 320) was processed using

the photogrammetry software. Visible RAD targets within the newly acquired set of photographs

were identified and assigned to the corresponding control point coordinates. With all control

points measured and photogrammetric processing complete, the locations (X, Y, Z) and

orientations (Omega, Phi, Kappa) for all 320 board camera stations were exported as a comma-

delimited text file. All future photograph acquisitions were assigned to the respective

photogrammetrically-derived camera locations and camera orientations listed in this file. These

steps served to establish a common 3D coordinate system for future photogrammetric

reconstructions.

7.6.3. Determination of Photograph-Capturing Intervals

Close-range photogrammetry of objects required not only full photographic coverage of

all specimen surfaces, but overlapping photographs such that all points to be measured were

107

clearly visible in at least two but ideally three or more photographs. To meet this requirement,

photographs were captured at specified intervals as the towers were manually rotated around the

specimen. It was desired to minimize the number of photographs required to reconstruct the

specimen, while maintaining a high degree of accuracy and precision. By increasing the base line

distance (and therefore rotation angle) between camera stations, the accuracy of measurements in

object space (i.e. on the specimen surface) was expected to increase. In turn, increasing the base

line distance reduced 1) the number of photographs and 2) the available overlap between

adjacent photographs. It was therefore desired to determine the optimal intervals at which

photographs should be captured. A sensitivity study was performed to determine the ideal angle

between adjacent sets of photographs. The study was conducted by placing a different analog

specimen (acrylic, 44.5 mm [1.75 in.] diameter by 88.9 mm [3.5 in.] length, nominal) into the

instrumented triaxial cell and capturing photographs of the specimen at five degree intervals (320

photographs, total). The larger specimen was selected because it represented the maximum

dimensions that would be achieved during large-strain triaxial compression tests (maximum

diameter) or extension tests (maximum height) on actual soil specimens. The cell remained

empty (air, instead of confining fluid) for this stage of the evaluation process. The sensitivity of

the camera stations to the angle between the photograph capturing intervals was evaluated for

45-, 30-, 15-, and five-degree intervals, which corresponded to 40, 60, 110, and 320 photographs,

respectively. These intervals were chosen because each interval was divisible by the next,

allowing for one common photoset to be used.

7.6.4. Capture of Photographs to Determine Accuracy in Confining Fluid

The same procedures that were utilized to 1) derive the board camera stations using the

brass analog specimen (in air) and to 2) determine the ideal angle between photos using the

108

large, acrylic analog specimen (also in air) were employed to evaluate the method in confining

fluid. A second, smaller acrylic analog specimen (38.1 mm [1.5 in.] diameter by 76.2 mm [3.0

in.] length, nominal) was submerged in confining fluid (silicone oil) within the triaxial cell for

the procedure. RAD-coded targets were printed on a sheet of temporary tattoo adhesive paper

and adhered to the surface of the acrylic specimen. The photogrammetry procedures that were

previously outlined in Section 7.6.2 were repeated and final camera stations were derived for all

future tests performed with the confining fluid-filled cell. This was necessary to ensure accuracy

of the camera stations when the cameras were submerged in the confining fluid. The coded

targets were removed and a different sequence of coded targets was adhered to the surface of

subsequent specimens. The new targets were used because it distinguished them from the targets

that were already identified to create the control point cloud (used to derive the camera stations).

The acrylic specimen was then placed within the triaxial cell filled with confining fluid once

more and photographs were captured to reconstruct the specimen. This second set of photographs

of the acrylic specimen was necessary because it would not have been a fair assessment to derive

the target locations on the surface of the specimen using the same photographs that were utilized

to derive the camera stations.

7.6.5. Photogrammetric Reconstruction of a Specimen

The photographs of the two acrylic analog specimens (large specimen used to evaluate

the sensitivity of the photograph-capturing interval and smaller specimen used to evaluate the

accuracy of the technique when subjected to the confining fluid) that were captured from within

the triaxial cell were processed within software to photogrammetrically reconstruct the

specimens. The photogrammetry projects that were created during the camera location and

orientation step, to establish the 3D coordinate system, were modified by replacing the

109

photographs within the existing projects with the newly acquired photographs of the acrylic

specimens. This ensured that the already derived camera stations (location and orientation)

remained constant, thereby enabling the greatest possible accuracy for the close-range

photogrammetry technique. Each visible target on the surface of the acrylic specimens was then

identified and measured in at least three photographs and assigned to the respective unique

identification number (384 and 283 total targets for the large- and small-acrylic specimens,

respectively). Once a target was measured in three or more photographs, three-dimensional

coordinates for that point were computed and reported by the software. The circular centers of

the targets provided a reliable means of identifying the precise locations of the targets. To aid in

the reliable identification of common points on the ends of the specimen, high contrast markers

were added to the porous stones on both ends of the specimen. The intersections between the

markers, the porous stones, and the ends of the specimen served to identify common points along

the ends of the specimen. Internal quality feedback within the software aided in identifying and

reducing point measurement errors, thereby 1) ensuring the quality of the photogrammetry

projects and 2) providing consistency among each of the projects that were processed. The

quality feedback metrics included total error, residuals, and point precision values.

After all of the points on the surfaces of the specimens were identified, radial curves were

drawn through the 3D points on the surface of the virtual specimens. Surface tools were utilized

to create outward-facing surfaces on the specimens; these surfaces were created by using the

curves as the edges of each surface, and to cap the open ends of the specimens. The virtual

specimens therefore took shape using the newly created surfaces; however, the photogrammetry

software did not correctly calculate the internal volumes of the virtual specimens, nor were the

surfaces “watertight”. The 3D models were therefore exported in a wavefront format (.obj

110

extension) to allow for further analysis using a software program that was more suited to

determining the accurate volume of a virtual object. A 3D computer-aided drawing (CAD)

software (Geomagic Design X 2015) was utilized for this purpose.

7.6.6. Determination of a Specimen Volume

Each 3D model exported from the photogrammetry software consisted of a number of

disconnected polygonal bands wrapped transversely around the surface of the model. Narrow

gaps between these polygonal bands were sealed using the global remesh and healing tools

within the software. The remesh tool worked by essentially shrink-wrapping the 3D model with a

new, improved surface that was free of holes, slivers, and other topologic imperfections. The

used software tools are proprietary but the results were similar to what would be expected from a

Poisson surface reconstruction, like that described by Kazhdan and Hoppe (2014). The settings

for this tool were adjusted so that the number of polygons that made up the output model was

100 times the number of polygons of the input model. The increase in the quantity of polygons

reduced the potential for rounding that was observed along sharp edges. Moreover, the healing

tool was then used to detect and remove any small clusters of free-floating polygons that were

not actually part of the surface of the models. After the final watertight models were created, the

calculation of the volume of each model was revealed when selecting on the properties of the

model. The exact method used to calculate volume by the software was not reported by the

software publishers, but the used method was likely similar to the process described by Mirtich

(1996).

7.6.7. Accuracy of Technique

To evaluate the accuracy of the internal cell photogrammetry approach, that is presented

herein, several other techniques were also employed to determine the volume of the smaller

111

acrylic analog specimen. The techniques included 1) the aforementioned internal

photogrammetry technique, 2) photogrammetry using DSLR camera obtained photographs only,

3) a 3D scanning technique, 4) manual measurements using a caliper and pi tape, and 5) a water-

displacement technique. Each of these not previously mentioned techniques (techniques 2-5) are

described in this section. Based on a review of the literature, no universal method exists to

evaluate the absolute or “true” accuracy of a volume determination technique. The amount of

difference relative to an external reference, often termed “error”, is only meaningful when the

nature of the external reference is reported. To provide a metric for comparison between the

volumes of the smaller acrylic specimen, as obtained using each technique, the difference was

evaluated relative to the water displacement technique. This technique was selected, because it

was based on well-established procedures documented in ASTM Standard D698 (ASTM 2012)

to determine the interior volume of a Proctor mold.

7.6.7.1. DSLR Camera Photogrammetry

For the DSLR camera survey technique, the smaller acrylic specimen was placed on a

table and approximately 40 photographs were captured of the specimen from various angles. The

photographs were imported into the photogrammetry software and a selection of the best photos

were processed. Common points (coded targets), on the surface of the specimen, were identified

and referenced to ensure that the points appeared in at least three photos. Measurements were

also imported to define the scale (known distance between select points). In a similar fashion to

the internal photogrammetry technique, surfaces were created on the virtual specimen and the

model was exported for processing and analyzed within the 3D CAD software.

112

7.6.7.2. 3D Scanning

By definition, 3D scanning is the use of a specialized instrument to rapidly record the 3D

information of an object or environment. A close-range 3D digitizing system (Breuckmann

SmartScan3D HE) that utilized fringe projection, or structured white light technology, was

employed to obtain the 3D data of the acrylic specimen. Specifically, a projector, two 5-

Megapixel color cameras, and multiple lenses were utilized to facilitate the 3D measurements. A

series of patterns (or fringes) were cast onto the specimen and the difference in the pattern from

each camera was utilized to compute a series of discrete measurements or 3D points. The

instrument captured approximately 150,000 points per individual scan.

The smaller acrylic specimen was scanned with a set of M-125 lenses (i.e. 125 mm

diagonal field of view at the optimal working distance of one meter). The M-125 lenses, the

highest resolution lenses available for this scanner, were used to achieve the highest possible

spatial resolution of approximately 60 μm horizontal. To begin the process of scanning, the

instrument was calibrated using 1) the prescribed procedure that was recommended by the

manufacturer, 2) a set of calibration targets, and 3) the companion 3D digitizing software

(OPTOCAT 2013R2). The calibration procedure reported an average accuracy of object points

of 15.41 μm in the X, 0.74 m in the Y, and 26.75 μm in the Z dimension (depth from scanner).

The specimen was made of an acrylic material that was partially transparent. To prevent scan

errors caused by light scattering during fringe projection, a thin coat of matte white spray paint

was applied to the specimen. Several spherical adhesive targets were also placed on each side of

the specimen to aid in the scan-to-scan alignment procedures during data processing. The

specimen was then placed at a 45-degree angle on an automated turntable (Figure 7.3) and

scanned at 20-degree intervals for a total of 18 scans. Two other manually positioned scans were

113

collected to fill in areas not visible during the turntable rotations. All of these data (20 scans)

were then processed using the digitizing software. The basic processing steps that were

performed included: 1) an iterative global best-fit alignment of all scans, 2) overlap reduction to

remove scan data collected at a high angle of incidence, 3) merging of individual scans to create

a single polygonal mesh, 4) smoothing to remove small amounts of noise and other scan

artifacts, and 5) hole-filling using the semi-automated tools that were available. The final 3D

model, as presented in Figure 7.3, was composed of approximately 685,000 polygonal faces and

approximately 343,000 vertices.

Figure 7.3. (a) Photograph of, and (b) three-dimensional, watertight model of small-acrylic

analog specimen with spherical adhesive targets (removed during processing), as obtained

during 3D scanning of specimen.

7.6.7.3. Manual Measurements

For the method that consisted of manual measurements, a linear caliper (with a resolution

of 0.05 mm) was used to measure the length of the acrylic specimen (average of three

measurements) and a pi tape (with a resolution of 0.01 mm) was used to measure the diameter of

the specimen (average of three measurements). The volume of the specimen was then calculated

based on the average measurements.

(a) (b)

114

7.6.7.4. Water Displacement

The same procedures that are commonly utilized to measure the volume of a Proctor

mold, as outlined in ASTM Standard D698 (ASTM 2012), were used to measure the volume of

the specimen. Specifically, after the volume of a Proctor mold was determined using the water-

filling method that is described in the Annex of the ASTM Standard, the specimen was placed

into the Proctor mold and submerged in de-ionized and de-aired water to determine the amount

of water that was displaced by the specimen. The mass of the acrylic specimen was determined

before and after water submersion to ensure that no water was imbibed by the specimen during

the testing.

7.6.8. Limitations and Sources of Error

The limitations of, and the identified sources of error associated with, the described

photogrammetry technique are discussed herein. The identified systematic errors were mitigated

during the process of collecting, processing, and evaluating data. Additionally, a schematic of the

relevant qualitative factors that influence the accuracy of photogrammetry applications is

presented as Figure 7.4.

115

Shading highlights the characteristics of the photogrammetry methodology presented in this study.

Figure 7.4. Qualitative factors affecting accuracy in photogrammetry (modified from Eos

Systems, Inc. 2015).

7.6.8.1. Precision of Repeat Interval Stops

Measured from a fixed starting position (in contact with the drainage lines), the camera

towers stopped at prescribed rotation intervals around the specimen to allow for repeat

occupation (during a given photogrammetry project and between successive photogrammetry

projects). The method relied upon the capture of photographs from the exact same locations with

each repetition, because photographs with known (derived) camera stations were replaced with

new photographs (thereby assigning the derived locations and orientations to the new

photographs). Although the same locations were reoccupied for each test, any deviation from the

photogrammetrically derived location could have resulted in error in the three-dimensional

coordinate of an observed point within the replaced photographs.

No

calibrationLess than

15 degrees

Few targets

per photo,

low

coverage

No targets,

all user

marked

Points

mostly on

only two

photos

Photo

RedundancyTargets

Camera

Resolution

Camera

Calibration

Method

Angles

between

Photos

Photo

Orientation

Quality

Expected

Accuracy

Lowest

Accuracy

Highest

Accuracy

11

Megapixel

5-6

MegapixelAverage

Accuracy

Video

640x480

Field

calibrated

camera

Most targets

on 8 or more

photos

35+ targets

per photo,

50-80%

coverage

Between 60

and 90

degrees

Some

naturally lit

targets

Retro-

reflective

Many good

quality

naturally lit

Calibrated

camera

Inverse

camera

All points on

3+ photos

15+ targets

per photo,

25- 60%

coverage

Between 15

and 60

degrees

116

7.6.8.2. Model Refinement

The number of targets that were utilized limited the mesh refinement of the surface of

each specimen. Furthermore, the number of targets that were utilized was related to processing

time and to the minimum size of targets. To maintain the automated target identification

capability of the photogrammetry software, a target center diameter of at least 30 pixels was

utilized. This resulted in the use of 286 targets that were evenly distributed (center to center

spacing of 5.65 mm) across the surfaces of the 38.1 mm (1.5 in.) in diameter by 76.2 mm (3.0

in.) in length (nominal) brass and acrylic soil specimens.

7.6.8.3. External Geometry Measurements

To scale a photogrammetry project, one or more external reference measurements was

required to be input. These reference measurements were in the form of a known distance

between two measured points located within the project. The resulting overall accuracy of a

project was therefore limited to the accuracy of the input measurements. To mitigate the impact

of this source of error, multiple reference measurements were made for various target pairs

within the project.

7.6.8.4. Determination of Specimen Ends

The most difficult aspect of processing the photographs of a specimen was the reliable

identification of the ends of the specimen (i.e. picking points along the edges at the two ends of

the specimen). Picking end points was challenging because distinct markers had to be identified

subjectively in adjacent photographs without the help of target centers. This challenge has often

been understated or not discussed in the literature, but should not be overlooked. To aid in the

reliable identification of specimen ends, high contrast markers were applied to the porous stones

on the ends of the specimens.

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7.7. Implementation of the Internal Photogrammetry Technique for Soil Specimens

Two undrained triaxial tests were performed on kaolinite soil specimens to assess the

viability of determining: 1) total and local strains, 2) total volume and volume changes at any

given stage of testing, and 3) the actual failure plane of a soil specimen. Specifically, one

undrained, conventional triaxial compression (CTC) test and one undrained, reduced triaxial

extension (RTE) test were conducted. The tests were performed with advanced, automated

triaxial apparatus that included pore water pressure and pore water volume measurements. In a

typical triaxial test, the exact total specimen volume at any given stage of testing (prior to

consolidation, prior to shearing, or during shearing), must be back-calculated from testing and

post-testing data using phase relationships and assumptions (most notably the right circular

cylinder assumption, see ASTM D4767-11, 2011). To illustrate this concept, a schematic of the

stages of a typical triaxial compression test is presented as Figure 7.5. This method of calculating

specimen volume often leads to erroneous results without any means of verification. The

implemented photogrammetry technique provided a means to independently determine the

volume of a soil specimen, during any desired stage of testing, without the need to rely upon

erroneous assumptions made during back-calculation.

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1. Pre-test: Mass (m) and water content (w), measured; Volume (V) calculated using caliper measurements. 2. Back-pressure saturation: Drain lines filled. Total volume change (ΔV) from pore pump measurements. This volume change includes air 1) purged from lines, and 2) going into suspension. 3. K0 Consolidation: Sample ΔV from pore pump measurements. 4. Shearing: m, w, and V assumed to be equal to post-test m, w, and V (if undrained); calculated from pore pump measurements (if drained). 5. Post-test: m and w, measured. Shear strength determined based on corrected area (Ac).

Figure 7.5. Typical measurements and calculations required to determine the phase

diagram of the soil specimen during a conventional triaxial compression test.

The soil specimens consisted of commercially available kaolinite soil (Kaowhite-S)

obtained from the Thiele Company (Sandersonville, Georgia). The specimens were slurry-

consolidated in an acrylic consolidometer under an overburden stress of 138 kPa (20 psi).

Specimens with nominal dimensions of 7.62 cm in length and 3.81 cm in diameter were extracted

from the consolidation apparatus and weighed. Using temporary tattoo paper, RAD-coded targets

were applied to the surface of the first membrane surrounding the sample. The membrane was then

placed onto the specimen, and a second membrane was applied over the first membrane (to reduce

the potential for liquid transfer or gas permeation). During the specimen preparation phase, care

was taken to minimize the amount of disturbance on the soil specimen. The confining cell was

filled with silicone oil, the top and bottom drain lines to the specimen were flushed to remove air

from the lines, and the specimen was back pressure saturated (B-check equal to 0.95 or higher)

before proceeding to the consolidation phase. During each test, the specimen was consolidated

under K0-conditions to a vertical effective stress of 310 kPa (45 psi). During consolidation, the

119

changes in pore pump volume measurements were used to determine changes in pore water volume

of the specimen. Upon completion of consolidation, the drain lines were closed and the specimen

was sheared under undrained conditions (strain rate of 0.5 percent per hour). For the CTC test, the

shearing was paused at intervals of 0, 2, 4, 6, 8, 11.5, and 15 percent axial strain. At each of these

strain intervals, the ten board cameras were used to capture photographs of the specimen at 20-

degree rotation intervals (total of 80 photographs per strain interval), as further discussed in

Section 7.8.2. Similarly, for the RTE test, the shearing was paused at intervals of -0, -2, -4, -6, -8,

-10, -12, -15 percent axial strain and photographs of the specimen were captured. For each strain

interval, the test was paused for less than 30 minutes. For completeness, a photograph of the

instrumented triaxial cell, as utilized in the RTE test, is presented (Fig. 7.6).

Processing procedures were identical to those employed to model the acrylic analog

specimen. After 3D models of the soil specimens were exported to wavefront format files, the

models were further analyzed within 3D CAD software. Local displacements on the surface of

each soil specimen were visualized using the built-in mesh deviation function. The software tool

likely functioned similar to the process described by Cignoni et al. (1998). Utilization of this

function allowed for watertight meshes to be overlayed (with a common coordinate system) to

compare the positive or negative changes between the surfaces of the two meshes. The post-

consolidation mesh was selected as the reference mesh for comparisons. A color-graded scale

was selected to visualize the magnitude of changes (cooler colors corresponded to negative

changes while warmer colors correlated to positive changes).

120

Figure 7.6. Photograph of the kaolinite specimen within the photogrammetrically

instrumented triaxial cell during the shearing stage of the extension test.

In addition to the undrained triaxial compression and triaxial extension tests, one

additional unconfined compression (UC) test was performed. The purpose of the UC test was to

compare 1) the calculated volumes during a test within the triaxial cell by utilizing the internal

photogrammetry technique, with 2) the calculated volumes during a test outside of the triaxial

cell utilizing the DSLR camera photogrammetry technique. The soil specimen was prepared in

an identical way to those specimens that were used in the two triaxial tests. RAD-coded targets

1. Load frame reaction rod (two quantity)

2. Cable with nine-pin feed-through connector

(four pins for the internal load cell, two pins

for the switchboard power supply, one pin for

the video signal, two pins unused)

3. Uplift prevention rod (two quantity, for

extension testing only)

4. Piston housing

5. Piston lock

6. Vacuum line for acrylic top cap vacuum

connection

7. Top platen of cell

8. Fastening rod (three quantity)

9. Piston

10. Switchboard for camera timing (as shown in

Salazar et al. [2015])

11. Electrical jumpers for individual camera power

supply (red)

12. Internal load cell

13. Electrical jumpers for common grounding and

video signals (green and yellow, respectively)

14. Acrylic top cap (triaxial extension vacuum cap

shown)

15. Drain line (connection to top cap)

16. Pore pressure transducer

17. Camera tower (two quantity, 5 cameras each)

18. Soil specimen within membrane (RAD-coded

targets adhered to membrane)

19. Rotating Delrin® bearing track

20. Top drain line and drain valve (black)

21. Bottom drain line and drain valve (red)

22. Cell pressure application line

1

2

3 4 5

6

7

12

15

16

17

18

22

14

19 20

21

13

11

10

9 8

121

were applied to the surface of the membrane and additional targets were placed on the loading

frame around the specimen to provide tie points for photogrammetric processing. The specimen

was sheared under unconfined conditions (although the specimen was wrapped in a membrane)

at a strain rate of 0.5 percent per hour. During the test, the shearing was paused at intervals of 0,

2, 4, 6, 8, 11.5, and 15 percent axial strain and approximately 40 photographs of the specimen

were captured at each strain interval. During the processing phase, the best 12 photos of the 40

photos that were captured for each strain interval, were selected and processed so that targets on

the surface of the specimen appeared in at least three photographs. Following the same

procedures as those used for the internal photogrammetry technique, 3D models were created

within photogrammetry software and were exported for further analysis within the 3D CAD

software.

7.8. Results and Discussion

The results from the evaluation of the internal cell photogrammetry technique are

presented herein. Furthermore, a discussion of the amount of error associated with the technique

and the sensitivity of the photograph-capturing interval are presented. The accuracy of the

utilized photogrammetry technique is discussed and the limitations are highlighted.

7.8.1. Volume Comparisons

The differences between the volumes determined using the various measurement

techniques (internal photogrammetry, DSLR photogrammetry, 3D scanning, manual

measurements) relative to the arbitrary reference technique (water displacement) fell within one-

half of one percent, as presented in Table 7.2. There was good agreement between the volumes

determined from the internal photogrammetry technique and reference technique (0.13 percent

difference). These difference values were expected to be greater for the techniques presented

122

herein than the difference values reported in the literature. This was expected because of the

relatively small size of the specimen that was utilized for evaluation of the internal

photogrammetry technique (nominal dimensions of 7.62 cm in length and 3.81 cm in diameter),

as compared to larger size specimens contained within the literature (typically, 10.16 cm in

length and 5.08 cm in diameter, or 14.22 cm in length and 7.11 cm in diameter). Despite the

increased sensitivity to volume determination error for the specimen used in this study, the

volume differences for all five measurement techniques were small (≤ 0.50 percent). The smaller

specimen size was utilized because of the reduced drainage distance, which significantly reduced

the time required for the completion of the consolidation phase of testing.

Based on a variety of tests conducted (prior to results reported in this study), the

repeatability of determining the volume of an analog specimen fell within 0.011 percent for the

3D scanning technique and within 0.084 percent for the internal photogrammetry technique.

Although the repeatability of the DSLR camera photogrammetry technique was not studied, it is

expected to be comparable to the repeatability of the internal photogrammetry technique.

Table 7.2. Comparison of small-acrylic analog specimen volumes as obtained using five

different techniques.

Volume Determination Method

Volume of Specimen [cm3] Mean [cm3]

Difference from Reference [%] Repetition

1 2 3

Water Displacement 94.97 95.60 95.47 95.35 Reference

Manual Measurements 95.82 95.82 95.82 95.82 0.50

3-D Scan 95.64 - - 95.64 0.31

DSLR Photogrammetry 95.62 - - 95.62 0.29

Internal Photogrammetry 95.22 - - 95.22 -0.13

123

7.8.2. Photograph Interval

Although it appeared that the repeatability of derived camera locations was sensitive to

the photograph interval (degree of separation between sets of photographs), as indicated by

convergence of camera locations in Figure 7.7, the effect was considered negligible (within

0.045 pixels for the maximum difference in camera location). The relationship between derived

camera orientation and photograph interval was not directly meaningful. Therefore, the influence

of the tower rotation interval on the determination of specimen volume was examined (Table

7.3). For the volume (as calculated from four photogrammetric reconstructions, using 45-, 30-,

15-, and five-degree photograph intervals), the standard deviation was equal to 0.34 cm3, and the

range was equal to 0.70 cm3. The determination of volume was therefore not sensitive to the

photograph interval. Thus, to 1) match the 20-degree gaps surrounding the drainage lines within

the triaxial cell, thereby providing consistent photograph intervals, and 2) maintain sufficient

overlap between photographs, an interval of 20 degrees was selected. This resulted in 80

photographs and approximately 240 minutes of processing time per test.

Table 7.3. Comparison of large-acrylic analog specimen volumes as determined during

internal photograph interval sensitivity test.

Rotation Interval

[Degrees]

Number of Photos

Computational Cost [minutes]

Specimen Volume

VT , [cm3] Summary Statistics

45 40 120 135.17 Mean Volume [cm3] 135.56

30 60 180 135.37 Standard Deviation [cm3] 0.34

15 110 330 135.87 Standard Error [cm3] 0.17

5 320 960 135.80 Coefficient of Variation [%] 0.25 Range [cm3] 0.70

Note: Photographs acquired using internal board cameras.

124

Figure 7.7. Sensitivity of derived camera location difference to interval between

photographs.

7.8.3. Testing of Internal Photogrammetry System on Soil Specimens

The volume of the various soil specimens was determined at numerous levels of axial

strain during both the CTC and RTE tests, as well as during the UC test. The CTC and RTE tests

were performed in an undrained condition and therefore the total volume of the specimen was

not expected to change during the shearing phase of each test. Likewise, the UC test was

undrained. The volumes that were measured during each test, and the summary statistics for each

test, supported this hypothesis. The results from the CTC test are presented in Table 7.4. The

volume change during the consolidation phase was determined to be 6.56 cm3, using the internal

photogrammetry technique. As a comparison, the volume change determined from the pore

pump measurements was equal to 6.81 cm3 (temperature corrected) and the change calculated

from the displacement transducer measurements was equal to 6.70 cm3 (using the assumption

that the cross-sectional area of the specimen remained constant during K0 consolidation). The

0

0.01

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0.03

0.04

0.05

0153045

Ca

me

ra L

oc

ati

on

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nc

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Photograph Interval [Degrees]

Average Difference

Maximum Difference

20

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125

internal photogrammetry approach therefore underpredicted the volume change by 3.7 percent,

as compared to the pore pump measurements, and by 2.1 percent, as compared to calculations

using the change in specimen height.

The results from the RTE test and the UC test are presented in Table 7.5 and Table 7.6,

respectively. For the CTC, RTE, and UC tests, the small changes in total volume, during

undrained shearing, were likely a result of the sensitivity to limited refinement of the 3D model

surface (function of the number of targets on the membrane). As indicated by the standard

deviation of total volumes calculated during the CTC test (0.37 cm3), as compared to the

standard deviation during the RTE test (0.27 cm3), the variability was greater for the CTC test.

The likely cause of the greater variability during the CTC test was that the target refinement was

more sensitive to the local deformations on the surface of the specimen during compression

(uneven bulging) than during extension (fairly uniform necking). Comparison with the results

from the UC test (standard deviation of 0.69 cm3) revealed that even with the high resolution

DSLR camera photogrammetry technique there was variability in the volumes, further

supporting the hypothesis that the model refinement (number and density of targets on surface of

the specimen) affected the accurate determination of specimen volume throughout a test.

126

Table 7.4. Volumes of kaolinite soil specimen as determined throughout the triaxial

compression test and corresponding summary statistics.

Testing Phase

Axial Strain εa , [%]

Volume VT , [cm3]

Summary Statistics

Consolidation Pre-consolidation 89.72 Change in Volume During

Consolidation [cm3] 6.56

0 83.16

Shear

2 82.92 Mean Volume During Shear [cm3]

83.37 4 83.28

6 83.27 Standard Deviation [cm3] 0.37

8 83.28 Standard Error [cm3] 0.14

11.5 84.10 Coefficient of Variation [%] 0.45

15 83.55 Range [cm3] 1.18


Table 7.5. Volumes of kaolinite soil specimen as determined throughout the triaxial

extension test and corresponding summary statistics.

Testing Phase


Volume VT , [cm3]

Summary Statistics

Shear

0 79.88 Mean Volume 80.30

8 80.40 During Shear [cm3]



15 80.64 Coefficient of Variation [%] 0.34

Range [cm3] 0.76


Table 7.6. Volumes of kaolinite soil specimen as determined throughout the unconfined

compression test and corresponding summary statistics.

Testing Phase


Volume VT , [cm3]

Summary Statistics

Shear

0 91.01 Mean Volume 91.35

2 91.46 During Shear [cm3]



8 90.75 Coefficient of Variation [%] 0.75

11.5 91.57 Range [cm3] 2.00

15 92.75

Note: Photographs acquired using DSLR camera.

127

The localized displacements of each specimen were visualized qualitatively for the CTC

and RTE tests. Specifically, the displacements were visualized for the consolidation phase of

testing, as presented in Figure 7.8, and for the shearing phase, as presented in Figure 7.9. During

the consolidation phase, the small strains in the radial direction of the specimen were somewhat

unexpected, as the triaxial testing apparatus was programmed for K0-consolidation by which the

diameter of the specimen should have remained constant throughout the consolidation phase of

the test. In the CTC test (Figure 7.9a), the actual failure plane of the soil specimen was evident

from the shear banding behavior at larger strains (greater than eight percent axial strain).

Conversely, necking behavior was observed for the specimen in the RTE test (Figure 7.9b).

Additional test data, including stress-strain and excess pore pressure relationships, were reported

in Salazar et al. (2017).

Figure 7.8. Visualization of photogrammetry-obtained, three-dimensional models of

kaolinite specimen during K0-consolidation phase of triaxial test (warm colors indicate

positive deformation and cool colors indicate negative deformation).

Pre-consolidation Post-consolidation

+2.175 mm -2.175 mm

128

Note: Photographs on the right are of post-test, oven-dried specimens.

Figure 7.9. Visualization of photogrammetry-obtained, three-dimensional models of

kaolinite test specimen during (a) conventional triaxial compression, and (b) reduced

triaxial extension tests up to 15 percent axial strain during shearing (warm colors indicate

positive deformation and cool colors indicate negative deformation).

Although the application of the internal photogrammetry technique required

modifications to a standard triaxial testing cell, the components of the system that were presented

were inexpensive, especially when compared with the cost of the triaxial testing equipment.

Furthermore, the technology associated with the modifications was not complex (Salazar and

Coffman 2015a, 2016 and Salazar et al. 2015). With the reduced computational cost of using less

photographs to reconstruct a given test specimen, the added data collection and processing time

was insignificant (hours) when compared with the total time (sample preparation, setup, testing,

Immediately Post-consolidated

εa = 0% εa = 2% εa = 8% εa = 15% εa = 6%

εa = -8% εa = -12% εa = -15% εa = -10%

(a)

(b)

Immediately Post-consolidated

εa = 0%

+2.175 mm -2.175 mm

129

and data reduction) for a typical triaxial test (weeks). Furthermore, the technique was no more

computationally costly than other photogrammetry methods found in the literature.

7.9. Conclusions

The internal cell photogrammetry technique was utilized to determine the volume of soil

specimens during all stages of undrained triaxial compression (CTC) and triaxial extension

(RTE) tests. The camera instrumentation, internal to the triaxial cell wall, allowed for direct

observation of the entire surface of the soil specimens throughout the triaxial tests and avoided

the need to correct for refraction and cell wall flexure involved with other methods in the

literature. The principles of close-range photogrammetry were utilized to enable accurate 3D

reconstructions of the soil specimens. Prior to triaxial testing, a variety of outside-of-cell volume

determination techniques, including DSLR camera photogrammetry, 3D scanning, manual

measurements, and water displacement techniques were employed to provide comparisons with

the volume of an acrylic analog specimen as determined utilizing the internal cell

photogrammetry technique. Results from the internal photogrammetry technique fell within 0.13

percent of the reference technique (water displacement) and results from all comparison

techniques fell within 0.50 percent. To minimize processing time to approximately 240 minutes,

a balance was struck between the number of photographs utilized (80 photographs total, 10

photographs captured at each 20 degree interval around a specimen) and the reliability in

photogrammetric measurements. 3D models were produced using commercially available

software and localized displacements that developed during the triaxial testing were visualized

and reported.

130

7.9.1. Potential Applications and Future Improvements

There are several potential applications for using the internal photogrammetry technique.

The approach may be utilized to provide verification of axial and radial strain measurements at

any point on the surface of the specimen or at the end cap connections. Furthermore, the strain-

based approach could be used in conjunction with 3D finite element analysis techniques to

predict the stress distribution throughout the specimen. This inverse solution will aid in

developing understanding into the constitutive models used to predict soil behavior.

Although other techniques may be used to measure total pore volume changes during

consolidation (i.e. pumps), these techniques may not necessarily be used to measure total volume

changes during shearing, nor will localized volume changes be captured. The technique

presented in this work may therefore be employed to monitor both total and local volume

changes during drained and undrained triaxial tests.

Future improvements to the internal photogrammetry system may facilitate increased

accuracy of the results. A higher degree of precision in the reoccupation of photograph interval

stops around the specimen would reduce error arising from the predetermined camera stations.

Therefore, a mechanized rotating track base is recommended for future applications.

Furthermore, future projects may also incorporate a geometric constraint that allows some small

amount of deviation from the known camera positions, but only along a modeled arc

representing the circular path of the camera track.

To increase the level of refinement on the surface of a specimen, a greater number of

targets may be required. However, the size of (and therefore the number of) the targets that were

utilized was limited, due to the resolution of the modified board camera devices. To reduce the

approximations between targets, improved camera resolution will allow for denser target

131

coverage on the specimen surface. Furthermore, improvements in automatic target identification

algorithms will result in reduced time required for processing.

7.10. Acknowledgements

This material is based upon work supported by the National Science Foundation Graduate

Research Fellowship under Grant No. DGE-1450079, as awarded to S.E. Salazar. The authors

would also like to acknowledge 1) support from the University of Arkansas Provost

Collaborative Research Grant awarded to R.A. Coffman (PI), M.L. Bernhardt (Co-PI) and A.

Barnes (Co-PI) and 2) undergraduate student support from the United States Department of

Transportation (USDOT) Office of the Assistant Secretary for Research and Technology (OST-

R) under Research and Innovation Technology Administration (RITA) Cooperative Agreement

Award No. OASRTRS-14-H-UARK awarded to R.A. Coffman (PI) and T. Oommen (Co-PI).

The views, opinions, findings, and conclusions reflected in this manuscript are the responsibility

of the authors only and do not represent the official policy or position of the USDOT/OST-R, or

any state or other entity.

132

7.11. References


Imaging Techniques,” J. Comput. Civil. Eng., Vol. 13, No. 2, pp. 103-109.


Specimens from Planar Images,” Comput-Aided. Civ. Inf., Vol. 16, No. 6, pp. 415–421.




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Triaxial Apparatus,” presented at the Fifth International Conference on Soil Mechanics

and Found Engineering, Paris, France, July 17-22, 1961, Dunod, Paris, pp. 13-21.

Cignoni, P., Rocchini, C., and Scopigno, R., 1998, “Metro: Measuring Error on Simplified

Surfaces,” Comp. Graph. Forum, Vol. 17, No. 2, pp. 167-174.



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133



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September 6-12, 1997, August Aimé Balkema, Amsterdam, pp. 185-188.





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Zhang, X., Li, L., Chen, G., and Lytton, R., 2015a, “A Photogrammetry-Based Method to



135

Zhang, X., Li, L., Chen, G., and Lytton, R., 2015b, “Reply to “Discussion of ‘A


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136

CHAPTER 8: CONCLUSIONS


Conclusions that were drawn from this work are contained in this chapter. Highlights

from the work are summarized in Section 8.2. The limitations of the work are outlined in Section

8.3. Finally, recommendations for future work are put forth in Section 8.4.

8.2. Highlights

The internal-cell photogrammetry technique that was developed in this work was

successfully applied to the monitoring of soil specimens during triaxial compression and triaxial

extension tests. Three-dimensional models with watertight meshes were derived from

photogrammetric processing. Measurements of total volume were obtained from each model.

The models developed for the specimen, when the specimen had been subjected to different

levels of axial stress, were differenced to quantify the development of axial, radial, and localized

deformations on the specimen surface during testing. Each set of measurements that were used to

derive a specimen volume was collected and processed independently. Therefore, the obtained

volume did not rely on assumptions of specimen dimensions or the deformation behavior during

the testing. This measurement technique reduced the source of systematic error in the

determination of specimen volume.

Volume measurements were made for a rigid reference (dummy) specimen, using five

independent techniques, to evaluate the internal-cell photogrammetry technique. Results for the

internal-cell photogrammetry technique fell within 0.13 percent of the reference technique and

within 0.50 percent of all other techniques. A sensitivity study was performed to examine the

effect that the number of photographs used in processing had on the total volume of the

specimen. The study revealed that a reduced number of photographs (from 320 to 80

137

photographs) was suitable for accurately reconstructing a specimen. Accordingly, this reduction

in photographs resulted in reduced processing time.

8.3. Limitations

Chapter 7 contained a detailed discussion of the limitations of the internal cell

photogrammetry technique and the sources of error that were identified. For reference, these

limitations included:

the precision of repeat interval stops (Section 7.6.8.1);

the refinement of specimen models (Section 7.6.8.2);

the accuracy of external geometry measurements (Section 7.6.8.3); and

the determination of specimen ends (Section 7.6.8.4).

In addition to the limitations discussed in Chapter 7, the following limitations of the work were

identified:

the lack of drained triaxial tests performed as part of this work;

the lack of repeat tests performed as part of this work;

the inability of the photogrammetry software to automatically identify all targets;

the amount of time required for photogrammetric processing of results;

the low resolution of the board camera devices; and

the poor performance of the board camera devices in low light conditions.

8.4. Recommendations

In accordance with the limitations that were identified in the previous section, the

following recommendations are made for future work.

The precision of the camera towers during repeat occupation should be improved with a

mechanized, rotating track (e.g. with a small stepper motor). This mechanization could

138

also foreseeably decrease the amount of time that the triaxial test is paused for during

acquisition of photographs.

The number/density of targets on the surface of the specimen should be increased. The

increase in density will increase the number of surveyed points and therefore also

increase the resolution of the three-dimensional model.

Although a comparison with other photogrammetric methods in the literature indicated

that the technique presented in this work was no more computationally costly, a reduction

in processing time is still desirable. It is therefore recommended that an alternative

(preferably) open-source software package be implemented for photogrammetric

processing that would allow for improved automatic target and texture detection.

Incorporating an improved board camera design in future iterations of the system could

foreseeably improve image resolution and sensor performance in low light conditions,

thereby improving the quality of the image data.

The strain measurements collected with this technique should be used in conjunction with

finite element analysis to predict the stress distribution throughout the soil specimen.

Such an inverse solution will help to develop a better understanding of the constitutive

behavior of the soil.

139

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